Factors of an integer: Difference between revisions
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==={{header|Minimal BASIC}}=== |
==={{header|Minimal BASIC}}=== |
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{{trans|GW-BASIC}} |
{{trans|GW-BASIC}} |
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{{works with|Nascom ROM BASIC|4.7}} |
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<lang gwbasic> |
<lang gwbasic> |
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10 REM Factors of an integer |
10 REM Factors of an integer |
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110 END |
110 END |
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</lang> |
</lang> |
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==={{header|Nascom BASIC}}=== |
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{{trans|GW-BASIC}} |
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{{works with|Nascom ROM BASIC|4.7}} |
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<lang basic> |
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10 REM Factors of an integer |
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20 INPUT "Enter an integer"; N |
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30 IF N=0 THEN 20 |
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40 NA=ABS(N) |
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50 FOR I=1 TO INT(NA/2) |
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60 IF NA=INT(NA/I)*I THEN PRINT I; |
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70 NEXT I |
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80 PRINT NA |
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90 END |
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</lang> |
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{{out}} |
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<pre> |
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Enter an integer? 60 |
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1 2 3 4 5 6 10 12 15 20 30 60 |
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</pre> |
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See also [[#Minimal BASIC|Minimal BASIC]] |
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==={{header|Sinclair ZX81 BASIC}}=== |
==={{header|Sinclair ZX81 BASIC}}=== |
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Revision as of 09:27, 17 March 2022
You are encouraged to solve this task according to the task description, using any language you may know.
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
- Task
Compute the factors of a positive integer.
These factors are the positive integers by which the number being factored can be divided to yield a positive integer result.
(Though the concepts function correctly for zero and negative integers, the set of factors of zero has countably infinite members, and the factors of negative integers can be obtained from the factors of related positive numbers without difficulty; this task does not require handling of either of these cases).
Note that every prime number has two factors: 1 and itself.
- Related tasks
- count in factors
- prime decomposition
- Sieve of Eratosthenes
- primality by trial division
- factors of a Mersenne number
- trial factoring of a Mersenne number
- partition an integer X into N primes
- sequence of primes by Trial Division
- sequence: smallest number greater than previous term with exactly n divisors
0815
<lang 0815> <:1:~>|~#:end:>~x}:str:/={^:wei:~%x<:a:x=$~ =}:wei:x<:1:+{>~>x=-#:fin:^:str:}:fin:{{~% </lang>
11l
<lang 11l>F factor(n)
V factors = Set[Int]()
L(x) 1..Int(sqrt(n))
I n % x == 0
factors.add(x)
factors.add(n I/ x)
R sorted(Array(factors))
L(i) (45, 53, 64)
print(i‘: factors: ’String(factor(i)))</lang>
- Output:
45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]
360 Assembly
Very compact version. <lang 360asm>* Factors of an integer - 07/10/2015 FACTOR CSECT
USING FACTOR,R15 set base register
LA R7,PG pgi=@pg
LA R6,1 i
L R3,N loop count
LOOP L R5,N n
LA R4,0
DR R4,R6 n/i
LTR R4,R4 if mod(n,i)=0
BNZ NEXT
XDECO R6,PG+120 edit i
MVC 0(6,R7),PG+126 output i
LA R7,6(R7) pgi=pgi+6
NEXT LA R6,1(R6) i=i+1
BCT R3,LOOP loop
XPRNT PG,120 print buffer
XR R15,R15 set return code
BR R14 return to caller
N DC F'12345' <== input value PG DC CL132' ' buffer
YREGS
END FACTOR</lang>
- Output:
1 3 5 15 823 2469 4115 12345
68000 Assembly
<lang 68000devpac>;max input range equals 0 to 0xFFFFFFFF.
jsr GetInput ;unimplemented routine to get user input for a positive (nonzero) integer.
;output of this routine will be in D0.
MOVE.L D0,D1 ;D1 will be used for temp storage. MOVE.L #1,D2 ;start with 1.
computeFactors: DIVU D2,D1 ;remainder is in top 2 bytes, quotient in bottom 2. MOVE.L D1,D3 ;temporarily store into D3 to check the remainder SWAP D3 ;swap the high and low words of D3. Now bottom 2 bytes contain remainder. CMP.W #0,D3 ;is the bottom word equal to 0? BNE D2_Wasnt_A_Divisor ;if not, D2 was not a factor of D1.
JSR PrintD2 ;unimplemented routine to print D2 to the screen as a decimal number.
D2_Wasnt_A_Divisor:
MOVE.L D0,D1 ;restore D1.
ADDQ.L #1,D2 ;increment D2
CMP.L D2,D1 ;is D2 now greater than D1?
BLS computeFactors ;if not, loop again
- end of program</lang>
AArch64 Assembly
<lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program factorst64.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc"
.equ CHARPOS, '@'
/*******************************************/ /* Initialized data */ /*******************************************/ .data szMessDeb: .ascii "Factors of : @ are : \n" szMessFactor: .asciz "@ \n" szCarriageReturn: .asciz "\n" /*******************************************/ /* UnInitialized data */ /*******************************************/ .bss sZoneConversion: .skip 100 /*******************************************/ /* code section */ /*******************************************/ .text .global main main: // entry of program
mov x0,#100 bl factors mov x0,#97 bl factors ldr x0,qNumber bl factors
100: // standard end of the program
mov x0, #0 // return code mov x8, #EXIT // request to exit program svc 0 // perform the system call
qNumber: .quad 32767 qAdrszCarriageReturn: .quad szCarriageReturn /******************************************************************/ /* calcul factors of number */ /******************************************************************/ /* x0 contains the number to factorize */ factors:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers
mov x5,x0 // limit calcul ldr x1,qAdrsZoneConversion // conversion register in decimal string bl conversion10S ldr x0,qAdrszMessDeb // display message ldr x1,qAdrsZoneConversion bl strInsertAtChar bl affichageMess mov x6,#1 // counter loop
1: // loop
udiv x0,x5,x6 // division
msub x3,x0,x6,x5 // compute remainder
cbnz x3,2f // remainder not = zero -> loop
// display result if yes
mov x0,x6
ldr x1,qAdrsZoneConversion
bl conversion10S
ldr x0,qAdrszMessFactor // display message
ldr x1,qAdrsZoneConversion
bl strInsertAtChar
bl affichageMess
2:
add x6,x6,#1 // add 1 to loop counter cmp x6,x5 // <= number ? ble 1b // yes loop
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret
qAdrszMessDeb: .quad szMessDeb qAdrszMessFactor: .quad szMessFactor qAdrsZoneConversion: .quad sZoneConversion /******************************************************************/ /* insert string at character insertion */ /******************************************************************/ /* x0 contains the address of string 1 */ /* x1 contains the address of insertion string */ /* x0 return the address of new string on the heap */ /* or -1 if error */ strInsertAtChar:
stp x2,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers stp x5,x6,[sp,-16]! // save registers stp x7,x8,[sp,-16]! // save registers mov x3,#0 // length counter
1: // compute length of string 1
ldrb w4,[x0,x3] cmp w4,#0 cinc x3,x3,ne // increment to one if not equal bne 1b // loop if not equal mov x5,#0 // length counter insertion string
2: // compute length to insertion string
ldrb w4,[x1,x5] cmp x4,#0 cinc x5,x5,ne // increment to one if not equal bne 2b // and loop cmp x5,#0 beq 99f // string empty -> error add x3,x3,x5 // add 2 length add x3,x3,#1 // +1 for final zero mov x6,x0 // save address string 1 mov x0,#0 // allocation place heap mov x8,BRK // call system 'brk' svc #0 mov x5,x0 // save address heap for output string add x0,x0,x3 // reservation place x3 length mov x8,BRK // call system 'brk' svc #0 cmp x0,#-1 // allocation error beq 99f mov x2,0 mov x4,0
3: // loop copy string begin
ldrb w3,[x6,x2] cmp w3,0 beq 99f cmp w3,CHARPOS // insertion character ? beq 5f // yes strb w3,[x5,x4] // no store character in output string add x2,x2,1 add x4,x4,1 b 3b // and loop
5: // x4 contains position insertion
add x8,x4,1 // init index character output string
// at position insertion + one
mov x3,#0 // index load characters insertion string
6:
ldrb w0,[x1,x3] // load characters insertion string cmp w0,#0 // end string ? beq 7f // yes strb w0,[x5,x4] // store in output string add x3,x3,#1 // increment index add x4,x4,#1 // increment output index b 6b // and loop
7: // loop copy end string
ldrb w0,[x6,x8] // load other character string 1 strb w0,[x5,x4] // store in output string cmp x0,#0 // end string 1 ? beq 8f // yes -> end add x4,x4,#1 // increment output index add x8,x8,#1 // increment index b 7b // and loop
8:
mov x0,x5 // return output string address b 100f
99: // error
mov x0,#-1
100:
ldp x7,x8,[sp],16 // restaur 2 registers ldp x5,x6,[sp],16 // restaur 2 registers ldp x3,x4,[sp],16 // restaur 2 registers ldp x2,lr,[sp],16 // restaur 2 registers ret
/********************************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc"
</lang>
ACL2
<lang Lisp>(defun factors-r (n i)
(declare (xargs :measure (nfix (- n i))))
(cond ((zp (- n i))
(list n))
((= (mod n i) 0)
(cons i (factors-r n (1+ i))))
(t (factors-r n (1+ i)))))
(defun factors (n)
(factors-r n 1))</lang>
Action!
<lang Action!>PROC PrintFactors(CARD a)
BYTE notFirst CARD p
p=1 notFirst=0
WHILE p<=a
DO
IF a MOD p=0 THEN
IF notFirst THEN
Print(", ")
FI
notFirst=1
PrintC(p)
FI
p==+1
OD
RETURN
PROC Test(CARD a)
PrintF("Factors of %U: ",a)
PrintFactors(a)
PutE()
RETURN
PROC Main()
Test(1) Test(101) Test(666) Test(1977) Test(2021) Test(6502) Test(12345)
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
Factors of 1: 1 Factors of 101: 1, 101 Factors of 666: 1, 2, 3, 6, 9, 18, 37,74, 111, 222, 333, 666 Factors of 1977: 1, 3, 659, 1977 Factors of 2021: 1, 43, 47, 2021 Factors of 6502: 1, 2, 3251, 6502 Factors of 12345: 1, 3, 5, 15, 823, 2469, 4115, 12345
ActionScript
<lang ActionScript>function factor(n:uint):Vector.<uint> { var factors:Vector.<uint> = new Vector.<uint>(); for(var i:uint = 1; i <= n; i++) if(n % i == 0)factors.push(i); return factors; }</lang>
Ada
<lang Ada>with Ada.Text_IO; with Ada.Command_Line; procedure Factors is
Number : Positive; Test_Nr : Positive := 1;
begin
if Ada.Command_Line.Argument_Count /= 1 then
Ada.Text_IO.Put (Ada.Text_IO.Standard_Error, "Missing argument!");
Ada.Command_Line.Set_Exit_Status (Ada.Command_Line.Failure);
return;
end if;
Number := Positive'Value (Ada.Command_Line.Argument (1));
Ada.Text_IO.Put ("Factors of" & Positive'Image (Number) & ": ");
loop
if Number mod Test_Nr = 0 then
Ada.Text_IO.Put (Positive'Image (Test_Nr) & ",");
end if;
exit when Test_Nr ** 2 >= Number;
Test_Nr := Test_Nr + 1;
end loop;
Ada.Text_IO.Put_Line (Positive'Image (Number) & ".");
end Factors;</lang>
Aikido
<lang aikido>import math
function factor (n:int) {
var result = []
function append (v) {
if (!(v in result)) {
result.append (v)
}
}
var sqrt = cast<int>(Math.sqrt (n))
append (1)
for (var i = n-1 ; i >= sqrt ; i--) {
if ((n % i) == 0) {
append (i)
append (n/i)
}
}
append (n)
return result.sort()
}
function printvec (vec) {
var comma = ""
print ("[")
foreach v vec {
print (comma + v)
comma = ", "
}
println ("]")
}
printvec (factor (45)) printvec (factor (25)) printvec (factor (100))</lang>
ALGOL 68
Note: The following implements generators, eliminating the need of declaring arbitrarily long int arrays for caching. <lang algol68>MODE YIELDINT = PROC(INT)VOID;
PROC gen factors = (INT n, YIELDINT yield)VOID: (
FOR i FROM 1 TO ENTIER sqrt(n) DO
IF n MOD i = 0 THEN
yield(i);
INT other = n OVER i;
IF i NE other THEN yield(n OVER i) FI
FI
OD
);
[]INT nums2factor = (45, 53, 64);
FOR i TO UPB nums2factor DO
INT num = nums2factor[i]; STRING sep := ": "; print(num);
- FOR INT j IN # gen factors(num, # ) DO ( #
- (INT j)VOID:(
print((sep,whole(j,0)));
sep:=", "
- OD # ));
print(new line)
OD</lang>
- Output:
+45: 1, 45, 3, 15, 5, 9
+53: 1, 53
+64: 1, 64, 2, 32, 4, 16, 8
ALGOL W
<lang algolw>begin
% return the factors of n ( n should be >= 1 ) in the array factor %
% the bounds of factor should be 0 :: len (len must be at least 1) %
% the number of factors will be returned in factor( 0 ) %
procedure getFactorsOf ( integer value n
; integer array factor( * )
; integer value len
) ;
begin
for i := 0 until len do factor( i ) := 0;
if n >= 1 and len >= 1 then begin
integer pos, lastFactor;
factor( 0 ) := factor( 1 ) := pos := 1;
% find the factors up to sqrt( n ) %
for f := 2 until truncate( sqrt( n ) ) + 1 do begin
if ( n rem f ) = 0 and pos <= len then begin
% found another factor and there's room to store it %
pos := pos + 1;
factor( 0 ) := pos;
factor( pos ) := f
end if_found_factor
end for_f;
% find the factors above sqrt( n ) %
lastFactor := factor( factor( 0 ) );
for f := factor( 0 ) step -1 until 1 do begin
integer newFactor;
newFactor := n div factor( f );
if newFactor > lastFactor and pos <= len then begin
% found another factor and there's room to store it %
pos := pos + 1;
factor( 0 ) := pos;
factor( pos ) := newFactor
end if_found_factor
end for_f;
end if_params_ok
end getFactorsOf ;
% prpocedure to test getFactorsOf %
procedure testFactorsOf( integer value n ) ;
begin
integer array factor( 0 :: 100 );
getFactorsOf( n, factor, 100 );
i_w := 1; s_w := 0; % set output format %
write( n, " has ", factor( 0 ), " factors:" );
for f := 1 until factor( 0 ) do writeon( " ", factor( f ) )
end testFactorsOf ;
% test the factorising % for i := 1 until 100 do testFactorsOf( i )
end.</lang>
- Output:
1 has 1 factors: 1 2 has 2 factors: 1 2 3 has 2 factors: 1 3 4 has 3 factors: 1 2 4 ... 96 has 12 factors: 1 2 3 4 6 8 12 16 24 32 48 96 97 has 2 factors: 1 97 98 has 6 factors: 1 2 7 14 49 98 99 has 6 factors: 1 3 9 11 33 99 100 has 9 factors: 1 2 4 5 10 20 25 50 100
ALGOL-M
Instead of displaying 1 and the number itself as factors, prime numbers are explicitly reported as such. To reduce the number of test divisions, only odd divisors are tested if an initial check shows the number to be factored is not even. The upper limit of divisors is set at N/2 or N/3, depending on whether N is even or odd, and is continuously reduced to N divided by the next potential divisor until the first factor is found. For a prime number the resulting limit will be the square root of N, which avoids the necessity of explicitly calculating that value. (ALGOL-M does not have a built-in square root function.) <lang algol> BEGIN
COMMENT RETURN P MOD Q; INTEGER FUNCTION MOD (P, Q); INTEGER P, Q; BEGIN
MOD := P - Q * (P / Q);
END;
INTEGER I, N, LIMIT, FOUND, START, DELTA;
WHILE 1 = 1 DO
BEGIN
WRITE ("NUMBER TO FACTOR (OR 0 TO QUIT):");
READ (N);
IF N = 0 THEN GOTO DONE;
WRITE ("THE FACTORS ARE:");
COMMENT CHECK WHETHER NUMBER IS EVEN OR ODD;
IF MOD(N, 2) = 0 THEN
BEGIN
START := 2;
DELTA := 1;
END
ELSE
BEGIN
START := 3;
DELTA := 2;
END;
COMMENT TEST POTENTIAL DIVISORS;
FOUND := 0;
I := START;
LIMIT := N / I;
WHILE I <= LIMIT DO
BEGIN
IF MOD(N, I) = 0 THEN
BEGIN
WRITEON (I);
FOUND := FOUND + 1;
END;
I := I + DELTA;
IF FOUND = 0 THEN LIMIT := N / I;
END;
IF FOUND = 0 THEN WRITEON (" NONE - THE NUMBER IS PRIME.");
WRITE("");
END;
DONE: WRITE ("GOODBYE");
END</lang>
- Output:
NUMBER TO FACTOR (OR 0 TO QUIT): -> 96 THE FACTORS ARE: 2 3 4 6 8 12 16 24 32 48 NUMBER TO FACTOR (OR 0 TO QUIT): -> 97 THE FACTORS ARE: NONE - THE NUMBER IS PRIME. NUMBER TO FACTOR (OR 0 TO QUIT): -> 98 THE FACTORS ARE: 2 7 14 49 NUMBER TO FACTOR (OR 0 TO QUIT): -> 0 GOODBYE
APL
<lang APL> factors←{(0=(⍳⍵)|⍵)/⍳⍵}
factors 12345
1 3 5 15 823 2469 4115 12345
factors 720
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720</lang>
AppleScript
Functional
<lang AppleScript>-- integerFactors :: Int -> [Int] on integerFactors(n)
if n = 1 then
{1}
else if 1 > n then
missing value
else
set realRoot to n ^ (1 / 2)
set intRoot to realRoot as integer
set blnPerfectSquare to intRoot = realRoot
-- isFactor :: Int -> Bool
script isFactor
on |λ|(x)
(n mod x) = 0
end |λ|
end script
-- Factors up to square root of n,
set lows to filter(isFactor, enumFromTo(1, intRoot))
-- integerQuotient :: Int -> Int
script integerQuotient
on |λ|(x)
(n / x) as integer
end |λ|
end script
-- and quotients of these factors beyond the square root.
lows & map(integerQuotient, ¬
items (1 + (blnPerfectSquare as integer)) thru -1 of reverse of lows)
end if
end integerFactors
TEST -------------------------
on run
integerFactors(120)
--> {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}
end run
GENERIC FUNCTIONS -------------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- filter :: (a -> Bool) -> [a] -> [a] on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn</lang>
- Output:
<lang AppleScript>{1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}</lang>
Straightforward
<lang applescript>on factors(n)
set output to {}
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set end of output to limit
set limit to limit - 1
end if
repeat with i from limit to 1 by -1
if (n mod i is 0) then
set beginning of output to i
set end of output to n div i
end if
end repeat
return output
end factors
factors(123456789)</lang>
- Output:
<lang applescript>{1, 3, 9, 3607, 3803, 10821, 11409, 32463, 34227, 13717421, 41152263, 123456789}</lang>
Arc
<lang Arc> (= divisor (fn (num)
(= dlist '())
(when (is 1 num) (= dlist '(1 0)))
(when (is 2 num) (= dlist '(2 1)))
(unless (or (is 1 num) (is 2 num))
(up i 1 (+ 1 (/ num 2))
(if (is 0 (mod num i))
(push i dlist)))
(= dlist (cons num dlist)))
dlist))
(map [rev _] (map [divisor _] '(45 53 60 64))) </lang>
- Output:
<lang Arc> '( (1 3 5 9 15 45) (1 53) (1 2 3 4 5 6 10 12 15 20 30 60) (1 2 4 8 16 32 64) ) </lang>
ARM Assembly
<lang ARM Assembly> /* ARM assembly Raspberry PI */ /* program factorst.s */
/* Constantes */ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ WRITE, 4 @ Linux syscall /* Initialized data */ .data szMessDeb: .ascii "Factors of :" sMessValeur: .fill 12, 1, ' '
.asciz "are : \n"
sMessFactor: .fill 12, 1, ' '
.asciz "\n"
szCarriageReturn: .asciz "\n"
/* UnInitialized data */ .bss
/* code section */ .text .global main main: /* entry of program */
push {fp,lr} /* saves 2 registers */
mov r0,#100
bl factors
mov r0,#97
bl factors
ldr r0,iNumber
bl factors
100: /* standard end of the program */
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
swi 0 @ perform the system call
iNumber: .int 32767 iAdrszCarriageReturn: .int szCarriageReturn /******************************************************************/ /* calcul factors of number */ /******************************************************************/ /* r0 contains the number */ factors:
push {fp,lr} /* save registres */
push {r1-r6} /* save others registers */
mov r5,r0 @ limit calcul
ldr r1,iAdrsMessValeur @ conversion register in decimal string
bl conversion10S
ldr r0,iAdrszMessDeb @ display message
bl affichageMess
mov r6,#1 @ counter loop
1: @ loop
mov r0,r5 @ dividende mov r1,r6 @ divisor bl division cmp r3,#0 @ remainder = zero ? bne 2f @ display result if yes mov r0,r6 ldr r1,iAdrsMessFactor bl conversion10S ldr r0,iAdrsMessFactor bl affichageMess
2:
add r6,#1 @ add 1 to loop counter cmp r6,r5 @ <= number ? ble 1b @ yes loop
100:
pop {r1-r6} /* restaur others registers */
pop {fp,lr} /* restaur des 2 registres */
bx lr /* return */
iAdrsMessValeur: .int sMessValeur iAdrszMessDeb: .int szMessDeb iAdrsMessFactor: .int sMessFactor /******************************************************************/ /* display text with size calculation */ /******************************************************************/ /* r0 contains the address of the message */ affichageMess:
push {fp,lr} /* save registres */
push {r0,r1,r2,r7} /* save others registers */
mov r2,#0 /* counter length */
1: /* loop length calculation */
ldrb r1,[r0,r2] /* read octet start position + index */
cmp r1,#0 /* if 0 its over */
addne r2,r2,#1 /* else add 1 in the length */
bne 1b /* and loop */
/* so here r2 contains the length of the message */
mov r1,r0 /* address message in r1 */
mov r0,#STDOUT /* code to write to the standard output Linux */
mov r7, #WRITE /* code call system "write" */
swi #0 /* call systeme */
pop {r0,r1,r2,r7} /* restaur others registers */
pop {fp,lr} /* restaur des 2 registres */
bx lr /* return */
/*=============================================*/ /* division integer unsigned */ /*============================================*/ division:
/* r0 contains N */
/* r1 contains D */
/* r2 contains Q */
/* r3 contains R */
push {r4, lr}
mov r2, #0 /* r2 ? 0 */
mov r3, #0 /* r3 ? 0 */
mov r4, #32 /* r4 ? 32 */
b 2f
1:
movs r0, r0, LSL #1 /* r0 ? r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1) */ adc r3, r3, r3 /* r3 ? r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C */ cmp r3, r1 /* compute r3 - r1 and update cpsr */ subhs r3, r3, r1 /* if r3 >= r1 (C=1) then r3 ? r3 - r1 */ adc r2, r2, r2 /* r2 ? r2 + r2 + C. This is equivalent to r2 ? (r2 << 1) + C */
2:
subs r4, r4, #1 /* r4 ? r4 - 1 */
bpl 1b /* if r4 >= 0 (N=0) then branch to .Lloop1 */
pop {r4, lr}
bx lr
/***************************************************/ /* conversion register in string décimal signed */ /***************************************************/ /* r0 contains the register */ /* r1 contains address of conversion area */ conversion10S:
push {fp,lr} /* save registers frame and return */
push {r0-r5} /* save other registers */
mov r2,r1 /* early storage area */
mov r5,#'+' /* default sign is + */
cmp r0,#0 /* négatif number ? */
movlt r5,#'-' /* yes sign is - */
mvnlt r0,r0 /* and inverse in positive value */
addlt r0,#1
mov r4,#10 /* area length */
1: /* conversion loop */
bl divisionpar10 /* division */ add r1,#48 /* add 48 at remainder for conversion ascii */ strb r1,[r2,r4] /* store byte area r5 + position r4 */ sub r4,r4,#1 /* previous position */ cmp r0,#0 bne 1b /* loop if quotient not equal zéro */ strb r5,[r2,r4] /* store sign at current position */ subs r4,r4,#1 /* previous position */ blt 100f /* if r4 < 0 end */ /* else complete area with space */ mov r3,#' ' /* character space */
2:
strb r3,[r2,r4] /* store byte */ subs r4,r4,#1 /* previous position */ bge 2b /* loop if r4 greather or equal zero */
100: /* standard end of function */
pop {r0-r5} /*restaur others registers */
pop {fp,lr} /* restaur des 2 registers frame et return */
bx lr
/***************************************************/ /* division par 10 signé */ /* Thanks to http://thinkingeek.com/arm-assembler-raspberry-pi/* /* and http://www.hackersdelight.org/ */ /***************************************************/ /* r0 contient le dividende */ /* r0 retourne le quotient */ /* r1 retourne le reste */ divisionpar10:
/* r0 contains the argument to be divided by 10 */
push {r2-r4} /* save autres registres */
mov r4,r0
ldr r3, .Ls_magic_number_10 /* r1 <- magic_number */
smull r1, r2, r3, r0 /* r1 <- Lower32Bits(r1*r0). r2 <- Upper32Bits(r1*r0) */
mov r2, r2, ASR #2 /* r2 <- r2 >> 2 */
mov r1, r0, LSR #31 /* r1 <- r0 >> 31 */
add r0, r2, r1 /* r0 <- r2 + r1 */
add r2,r0,r0, lsl #2 /* r2 <- r0 * 5 */
sub r1,r4,r2, lsl #1 /* r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) */
pop {r2-r4}
bx lr /* leave function */
.align 4
.Ls_magic_number_10: .word 0x66666667
</lang>
Arturo
<lang rebol>factors: $[num][ select 1..num [x][ (num%x)=0 ] ]
print factors 36</lang>
- Output:
1 2 3 4 6 9 12 18 36
AutoHotkey
<lang AutoHotkey>msgbox, % factors(45) "`n" factors(53) "`n" factors(64)
Factors(n) { Loop, % floor(sqrt(n))
{ v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index
}
Sort, v, N U D,
Return, v
}</lang>
- Output:
1,3,5,9,15,45 1,53 1,2,4,8,16,32,64
AutoIt
<lang AutoIt>;AutoIt Version: 3.2.10.0 $num = 45 MsgBox (0,"Factors", "Factors of " & $num & " are: " & factors($num)) consolewrite ("Factors of " & $num & " are: " & factors($num)) Func factors($intg)
$ls_factors=""
For $i = 1 to $intg/2
if ($intg/$i - int($intg/$i))=0 Then
$ls_factors=$ls_factors&$i &", "
EndIf Next Return $ls_factors&$intg
EndFunc</lang>
- Output:
Factors of 45 are: 1, 3, 5, 9, 15, 45
AWK
<lang AWK>
- syntax: GAWK -f FACTORS_OF_AN_INTEGER.AWK
BEGIN {
print("enter a number or C/R to exit")
} { if ($0 == "") { exit(0) }
if ($0 !~ /^[0-9]+$/) {
printf("invalid: %s\n",$0)
next
}
n = $0
printf("factors of %s:",n)
for (i=1; i<=n; i++) {
if (n % i == 0) {
printf(" %d",i)
}
}
printf("\n")
} </lang>
- Output:
enter a number or C/R to exit invalid: -1 factors of 0: factors of 1: 1 factors of 2: 1 2 factors of 11: 1 11 factors of 64: 1 2 4 8 16 32 64 factors of 100: 1 2 4 5 10 20 25 50 100 factors of 32766: 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 factors of 32767: 1 7 31 151 217 1057 4681 32767
BASIC
This example stores the factors in a shared array (with the original number as the last element) for later retrieval.
Note that this will error out if you pass 32767 (or higher). <lang qbasic>DECLARE SUB factor (what AS INTEGER)
REDIM SHARED factors(0) AS INTEGER
DIM i AS INTEGER, L AS INTEGER
INPUT "Gimme a number"; i
factor i
PRINT factors(0); FOR L = 1 TO UBOUND(factors)
PRINT ","; factors(L);
NEXT PRINT
SUB factor (what AS INTEGER)
DIM tmpint1 AS INTEGER DIM L0 AS INTEGER, L1 AS INTEGER
REDIM tmp(0) AS INTEGER REDIM factors(0) AS INTEGER factors(0) = 1
FOR L0 = 2 TO what
IF (0 = (what MOD L0)) THEN
'all this REDIMing and copying can be replaced with:
'REDIM PRESERVE factors(UBOUND(factors)+1)
'in languages that support the PRESERVE keyword
REDIM tmp(UBOUND(factors)) AS INTEGER
FOR L1 = 0 TO UBOUND(factors)
tmp(L1) = factors(L1)
NEXT
REDIM factors(UBOUND(factors) + 1)
FOR L1 = 0 TO UBOUND(factors) - 1
factors(L1) = tmp(L1)
NEXT
factors(UBOUND(factors)) = L0
END IF
NEXT
END SUB</lang>
- Output:
Gimme a number? 17 1 , 17 Gimme a number? 12345 1 , 3 , 5 , 15 , 823 , 2469 , 4115 , 12345 Gimme a number? 32765 1 , 5 , 6553 , 32765 Gimme a number? 32766 1 , 2 , 3 , 6 , 43 , 86 , 127 , 129 , 254 , 258 , 381 , 762 , 5461 , 10922 , 16383 , 32766
ASIC
<lang basic> REM Factors of an integer PRINT "Enter an integer"; LOOP:
INPUT N IF N = 0 THEN LOOP:
NA = ABS(N) NDIV2 = NA / 2 FOR I = 1 TO NDIV2
NMODI = NA MOD I IF NMODI = 0 THEN PRINT I; ENDIF
NEXT I PRINT NA END</lang>
- Output:
Enter an integer?60
1 2 3 4 5 6 10 12 15 20 30 60
BASIC256
<lang BASIC256> subroutine printFactors(n)
print n; " => ";
for i = 1 to n / 2
if n mod i = 0 then print i; " ";
next i
print n
end subroutine
call printFactors(11) call printFactors(21) call printFactors(32) call printFactors(45) call printFactors(67) call printFactors(96) end </lang>
- Output:
Igual que la entrada de FreeBASIC.
GW-BASIC
<lang gwbasic> 10 INPUT "Enter an integer: ", N 20 IF N = 0 THEN GOTO 10 30 NA = ABS(N) 40 FOR I = 1 TO NA/2 50 IF NA MOD I = 0 THEN PRINT I; 60 NEXT I 70 PRINT NA</lang>
- Output:
Enter an integer: 1 1 Enter an integer: 12 1 2 3 4 6 12 Enter an integer: 13 1 13 Enter an integer: -22222 1 2 41 82 271 542 11111 22222
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Factors.bas" 110 INPUT PROMPT "Number: ":N 120 FOR I=1 TO INT(N/2) 130 IF MOD(N,I)=0 THEN PRINT I; 140 NEXT 150 PRINT N</lang>
Minimal BASIC
<lang gwbasic> 10 REM Factors of an integer 20 PRINT "Enter an integer"; 30 INPUT N 40 IF N = 0 THEN 30 50 N1 = ABS(N) 60 FOR I = 1 TO N1/2 70 IF INT(N1/I)*I <> N1 THEN 90 80 PRINT I; 90 NEXT I 100 PRINT N1 110 END </lang>
Nascom BASIC
<lang basic> 10 REM Factors of an integer 20 INPUT "Enter an integer"; N 30 IF N=0 THEN 20 40 NA=ABS(N) 50 FOR I=1 TO INT(NA/2) 60 IF NA=INT(NA/I)*I THEN PRINT I; 70 NEXT I 80 PRINT NA 90 END </lang>
- Output:
Enter an integer? 60 1 2 3 4 5 6 10 12 15 20 30 60
See also Minimal BASIC
Sinclair ZX81 BASIC
<lang basic>10 INPUT N 20 FOR I=1 TO N 30 IF N/I=INT (N/I) THEN PRINT I;" "; 40 NEXT I</lang>
- Input:
315
- Output:
1 3 5 7 9 15 35 45 63 105 315
Tiny BASIC
<lang Tiny BASIC>100 PRINT "Give me a number:" 110 INPUT I 120 LET C=1 130 PRINT "Factors of ",I,":" 140 IF I/C*C=I THEN PRINT C 150 LET C=C+1 160 IF C<=I THEN GOTO 140 170 END</lang>
- Output:
Give me a number: 60 Factors of 60: 1 2 3 4 5 6 10 12 15 20 30 60
True BASIC
<lang qbasic> sub printfactors(n)
if n < 1 then exit sub
print n; "=>";
for i = 1 to n / 2
if remainder(n, i) = 0 then print i;
next i
print n
end sub
call printfactors(11) call printfactors(21) call printfactors(32) call printfactors(45) call printfactors(67) call printfactors(96) print end </lang>
- Output:
Igual que la entrada de FreeBASIC.
Batch File
Command line version: <lang dos>@echo off set res=Factors of %1: for /L %%i in (1,1,%1) do call :fac %1 %%i echo %res% goto :eof
- fac
set /a test = %1 %% %2 if %test% equ 0 set res=%res% %2</lang>
- Output:
>factors 32767 Factors of 32767: 1 7 31 151 217 1057 4681 32767 >factors 45 Factors of 45: 1 3 5 9 15 45 >factors 53 Factors of 53: 1 53 >factors 64 Factors of 64: 1 2 4 8 16 32 64 >factors 100 Factors of 100: 1 2 4 5 10 20 25 50 100
Interactive version: <lang dos>@echo off set /p limit=Gimme a number: set res=Factors of %limit%: for /L %%i in (1,1,%limit%) do call :fac %limit% %%i echo %res% goto :eof
- fac
set /a test = %1 %% %2 if %test% equ 0 set res=%res% %2</lang>
- Output:
>factors Gimme a number:27 Factors of 27: 1 3 9 27 >factors Gimme a number:102 Factors of 102: 1 2 3 6 17 34 51 102
BBC BASIC
<lang bbcbasic> INSTALL @lib$+"SORTLIB"
sort% = FN_sortinit(0, 0)
PRINT "The factors of 45 are " FNfactorlist(45)
PRINT "The factors of 12345 are " FNfactorlist(12345)
END
DEF FNfactorlist(N%)
LOCAL C%, I%, L%(), L$
DIM L%(32)
FOR I% = 1 TO SQR(N%)
IF (N% MOD I% = 0) THEN
L%(C%) = I%
C% += 1
IF (N% <> I%^2) THEN
L%(C%) = (N% DIV I%)
C% += 1
ENDIF
ENDIF
NEXT I%
CALL sort%, L%(0)
FOR I% = 0 TO C%-1
L$ += STR$(L%(I%)) + ", "
NEXT
= LEFT$(LEFT$(L$))</lang>
- Output:
The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345
bc
<lang bc>/* Calculate the factors of n and return their count.
* This function mutates the global array f[] which will * contain all factors of n in ascending order after the call! */
define f(n) {
auto i, d, h, h[], l, o
/* Local variables:
* i: Loop variable.
* d: Complementary (higher) factor to i.
* h: Will always point to the last element of h[].
* h[]: Array to hold the greater factor of the pair (x, y), where
* x * y == n. The factors are stored in descending order.
* l: Will always point to the next free spot in f[].
* o: For saving the value of scale.
*/
/* Use integer arithmetic */ o = scale scale = 0
/* Two factors are 1 and n (if n != 1) */ f[l++] = 1 if (n == 1) return(1) h[0] = n
/* Main loop */
for (i = 2; i < h[h]; i++) {
if (n % i == 0) {
d = n / i
if (d != i) {
h[++h] = d
}
f[l++] = i
}
}
/* Append the values in h[] to f[] */
while (h >= 0) {
f[l++] = h[h--]
}
scale = o return(l)
}</lang>
Befunge
<lang Befunge>10:p&v: >:0:g%#v_0:g\:0:g/\v
>:0:g:*`| > >0:g1+0:p
>:0:g:*-#v_0:g\>$>:!#@_.v
> ^ ^ ," "<</lang>
BQN
A bqncrate idiom.
<lang bqn>Factors ← (1+↕)⊸(⊣/˜0=|)
•Show Factors 12345 •Show Factors 729</lang> <lang>⟨ 1 3 5 15 823 2469 4115 12345 ⟩ ⟨ 1 3 9 27 81 243 729 ⟩</lang>
The primes library from bqn-libs can be used for a solution that's more efficient for large inputs. FactorExponents returns each unique prime factor along with its exponent.
<lang bqn>⟨FactorExponents⟩ ← •Import "primes.bqn" # With appropriate path
Factors ← { ∧⥊ 1 ×⌜´ ⋆⟜(↕1+⊢)¨˝ FactorExponents 𝕩 }</lang>
Burlesque
<lang burlesque>blsq ) 32767 fc {1 7 31 151 217 1057 4681 32767}</lang>
C
<lang c>#include <stdio.h>
- include <stdlib.h>
typedef struct {
int *list; short count;
} Factors;
void xferFactors( Factors *fctrs, int *flist, int flix ) {
int ix, ij;
int newSize = fctrs->count + flix;
if (newSize > flix) {
fctrs->list = realloc( fctrs->list, newSize * sizeof(int));
}
else {
fctrs->list = malloc( newSize * sizeof(int));
}
for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) {
fctrs->list[ix] = flist[ij];
}
fctrs->count = newSize;
}
Factors *factor( int num, Factors *fctrs) {
int flist[301], flix;
int dvsr;
flix = 0;
fctrs->count = 0;
free(fctrs->list);
fctrs->list = NULL;
for (dvsr=1; dvsr*dvsr < num; dvsr++) {
if (num % dvsr != 0) continue;
if ( flix == 300) {
xferFactors( fctrs, flist, flix );
flix = 0;
}
flist[flix++] = dvsr;
flist[flix++] = num/dvsr;
}
if (dvsr*dvsr == num)
flist[flix++] = dvsr;
if (flix > 0)
xferFactors( fctrs, flist, flix );
return fctrs;
}
int main(int argc, char*argv[]) {
int nums2factor[] = { 2059, 223092870, 3135, 45 };
Factors ftors = { NULL, 0};
char sep;
int i,j;
for (i=0; i<4; i++) {
factor( nums2factor[i], &ftors );
printf("\nfactors of %d are:\n ", nums2factor[i]);
sep = ' ';
for (j=0; j<ftors.count; j++) {
printf("%c %d", sep, ftors.list[j]);
sep = ',';
}
printf("\n");
}
return 0;
}</lang>
Prime factoring
<lang C>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
/* 65536 = 2^16, so we can factor all 32 bit ints */ char bits[65536];
typedef unsigned long ulong; ulong primes[7000], n_primes;
typedef struct { ulong p, e; } prime_factor; /* prime, exponent */
void sieve() { int i, j; memset(bits, 1, 65536); bits[0] = bits[1] = 0; for (i = 0; i < 256; i++) if (bits[i]) for (j = i * i; j < 65536; j += i) bits[j] = 0;
/* collect primes into a list. slightly faster this way if dealing with large numbers */ for (i = j = 0; i < 65536; i++) if (bits[i]) primes[j++] = i;
n_primes = j; }
int get_prime_factors(ulong n, prime_factor *lst) { ulong i, e, p; int len = 0;
for (i = 0; i < n_primes; i++) { p = primes[i]; if (p * p > n) break; for (e = 0; !(n % p); n /= p, e++); if (e) { lst[len].p = p; lst[len++].e = e; } }
return n == 1 ? len : (lst[len].p = n, lst[len].e = 1, ++len); }
int ulong_cmp(const void *a, const void *b) { return *(const ulong*)a < *(const ulong*)b ? -1 : *(const ulong*)a > *(const ulong*)b; }
int get_factors(ulong n, ulong *lst) { int n_f, len, len2, i, j, k, p; prime_factor f[100];
n_f = get_prime_factors(n, f);
len2 = len = lst[0] = 1; /* L = (1); L = (L, L * p**(1 .. e)) forall((p, e)) */ for (i = 0; i < n_f; i++, len2 = len) for (j = 0, p = f[i].p; j < f[i].e; j++, p *= f[i].p) for (k = 0; k < len2; k++) lst[len++] = lst[k] * p;
qsort(lst, len, sizeof(ulong), ulong_cmp); return len; }
int main() { ulong fac[10000]; int len, i, j; ulong nums[] = {3, 120, 1024, 2UL*2*2*2*3*3*3*5*5*7*11*13*17*19 };
sieve();
for (i = 0; i < 4; i++) { len = get_factors(nums[i], fac); printf("%lu:", nums[i]); for (j = 0; j < len; j++) printf(" %lu", fac[j]); printf("\n"); }
return 0; }</lang>
- Output:
3: 1 3 120: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 1024: 1 2 4 8 16 32 64 128 256 512 1024 3491888400: 1 2 3 4 5 6 7 8 9 10 11 ...(>1900 numbers)... 1163962800 1745944200 3491888400
C#
C# 1.0
<lang csharp>static void Main (string[] args) {
do {
Console.WriteLine ("Number:");
Int64 p = 0;
do {
try {
p = Convert.ToInt64 (Console.ReadLine ());
break;
} catch (Exception) { }
} while (true);
Console.WriteLine ("For 1 through " + ((int) Math.Sqrt (p)).ToString () + "");
for (int x = 1; x <= (int) Math.Sqrt (p); x++) {
if (p % x == 0)
Console.WriteLine ("Found: " + x.ToString () + ". " + p.ToString () + " / " + x.ToString () + " = " + (p / x).ToString ());
}
Console.WriteLine ("Done.");
} while (true);
}</lang>
C# 3.0
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
public static class Extension {
public static List<int> Factors (this int me) {
return Enumerable.Range (1, me).Where (x => me % x == 0).ToList ();
}
}
class Program {
static void Main (string[] args) {
Console.WriteLine (String.Join (", ", 45. Factors ()));
}
}</lang>
- Output:
Number: 32434243 For 1 through 5695 Found: 1. 32434243 / 1 = 32434243 Found: 307. 32434243 / 307 = 105649 Done.
C++
<lang cpp>#include <iostream>
- include <iomanip>
- include <vector>
- include <algorithm>
- include <iterator>
std::vector<int> GenerateFactors(int n) {
std::vector<int> factors = { 1, n };
for (int i = 2; i * i <= n; ++i) {
if (n % i == 0) {
factors.push_back(i);
if (i * i != n)
factors.push_back(n / i);
}
}
std::sort(factors.begin(), factors.end()); return factors;
}
int main() {
const int SampleNumbers[] = { 3135, 45, 60, 81 };
for (size_t i = 0; i < sizeof(SampleNumbers) / sizeof(int); ++i) {
std::vector<int> factors = GenerateFactors(SampleNumbers[i]);
std::cout << "Factors of ";
std::cout.width(4);
std::cout << SampleNumbers[i] << " are: ";
std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
}
return EXIT_SUCCESS;
}</lang>
- Output:
Factors of 3135 are: 1 3 5 11 15 19 33 55 57 95 165 209 285 627 1045 3135 Factors of 45 are: 1 3 5 9 15 45 Factors of 60 are: 1 2 3 4 5 6 10 12 15 20 30 60 Factors of 81 are: 1 3 9 27 81
Ceylon
<lang ceylon>shared void run() { {Integer*} getFactors(Integer n) => (1..n).filter((Integer element) => element.divides(n));
for(Integer i in 1..100) { print("the factors of ``i`` are ``getFactors(i)``"); } }</lang>
Chapel
Inspired by the Clojure solution: <lang chapel>iter factors(n) { for i in 1..floor(sqrt(n)):int { if n % i == 0 then { yield i; yield n / i; } } }</lang>
Clojure
<lang lisp>(defn factors [n] (filter #(zero? (rem n %)) (range 1 (inc n))))
(print (factors 45))</lang>
(1 3 5 9 15 45)
Improved version. Considers small factors from 1 up to (sqrt n) -- we increment it because range does not include the end point. Pair each small factor with its co-factor, flattening the results, and put them into a sorted set to get the factors in order. <lang lisp>(defn factors [n]
(into (sorted-set)
(mapcat (fn [x] [x (/ n x)])
(filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))</lang>
Same idea, using for comprehensions. <lang lisp>(defn factors [n]
(into (sorted-set)
(reduce concat
(for [x (range 1 (inc (Math/sqrt n))) :when (zero? (rem n x))]
[x (/ n x)]))))</lang>
CLU
<lang clu>isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
x1: int := (x0 + s/x0)/2
while x1<x0 do
x0, x1 := x1, (x1 + s/x1)/2
end
return(x0)
end isqrt
factors = iter (n: int) yields (int)
yield(1)
for i: int in int$from_to(2,isqrt(n)) do
if n//i=0 then
yield(i)
if i*i ~= n then yield(n/i) end
end
end
yield(n)
end factors
start_up = proc ()
po: stream := stream$primary_output()
a: array[int] := array[int]$[3135, 45, 64, 53, 45, 81]
for n: int in array[int]$elements(a) do
stream$puts(po, "Factors of " || int$unparse(n) || ":")
for f: int in factors(n) do
stream$puts(po, " " || int$unparse(f))
end
stream$putl(po, "")
end
end start_up</lang>
- Output:
Factors of 3135: 1 3 1045 5 627 11 285 15 209 19 165 33 95 55 57 3135 Factors of 45: 1 3 15 5 9 45 Factors of 64: 1 2 32 4 16 8 64 Factors of 53: 1 53 Factors of 45: 1 3 15 5 9 45 Factors of 81: 1 3 27 9 81
COBOL
<lang cobol>
IDENTIFICATION DIVISION.
PROGRAM-ID. FACTORS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATING.
03 NUM USAGE BINARY-LONG VALUE ZERO.
03 LIM USAGE BINARY-LONG VALUE ZERO.
03 CNT USAGE BINARY-LONG VALUE ZERO.
03 DIV USAGE BINARY-LONG VALUE ZERO.
03 REM USAGE BINARY-LONG VALUE ZERO.
03 ZRS USAGE BINARY-SHORT VALUE ZERO.
01 DISPLAYING.
03 DIS PIC 9(10) USAGE DISPLAY.
PROCEDURE DIVISION.
MAIN-PROCEDURE.
DISPLAY "Factors of? " WITH NO ADVANCING
ACCEPT NUM
DIVIDE NUM BY 2 GIVING LIM.
PERFORM VARYING CNT FROM 1 BY 1 UNTIL CNT > LIM
DIVIDE NUM BY CNT GIVING DIV REMAINDER REM
IF REM = 0
MOVE CNT TO DIS
PERFORM SHODIS
END-IF
END-PERFORM.
MOVE NUM TO DIS.
PERFORM SHODIS.
STOP RUN.
SHODIS.
MOVE ZERO TO ZRS.
INSPECT DIS TALLYING ZRS FOR LEADING ZERO.
DISPLAY DIS(ZRS + 1:)
EXIT PARAGRAPH.
END PROGRAM FACTORS.
</lang>
CoffeeScript
<lang coffeescript># Reference implementation for finding factors is slow, but hopefully
- robust--we'll use it to verify the more complicated (but hopefully faster)
- algorithm.
slow_factors = (n) ->
(i for i in [1..n] when n % i == 0)
- The rest of this code does two optimizations:
- 1) When you find a prime factor, divide it out of n (smallest_prime_factor).
- 2) Find the prime factorization first, then compute composite factors from those.
smallest_prime_factor = (n) ->
for i in [2..n] return n if i*i > n return i if n % i == 0
prime_factors = (n) ->
return {} if n == 1
spf = smallest_prime_factor n
result = prime_factors(n / spf)
result[spf] or= 0
result[spf] += 1
result
fast_factors = (n) ->
prime_hash = prime_factors n
exponents = []
for p of prime_hash
exponents.push
p: p
exp: 0
result = []
while true
factor = 1
for obj in exponents
factor *= Math.pow obj.p, obj.exp
result.push factor
break if factor == n
# roll the odometer
for obj, i in exponents
if obj.exp < prime_hash[obj.p]
obj.exp += 1
break
else
obj.exp = 0
return result.sort (a, b) -> a - b
verify_factors = (factors, n) ->
expected_result = slow_factors n
throw Error("wrong length") if factors.length != expected_result.length
for factor, i in expected_result
console.log Error("wrong value") if factors[i] != factor
for n in [1, 3, 4, 8, 24, 37, 1001, 11111111111, 99999999999]
factors = fast_factors n console.log n, factors if n < 1000000 verify_factors factors, n</lang>
- Output:
> coffee factors.coffee 1 [ 1 ] 3 [ 1, 3 ] 4 [ 1, 2, 4 ] 8 [ 1, 2, 4, 8 ] 24 [ 1, 2, 3, 4, 6, 8, 12, 24 ] 37 [ 1, 37 ] 1001 [ 1, 7, 11, 13, 77, 91, 143, 1001 ] 11111111111 [ 1, 21649, 513239, 11111111111 ] 99999999999 [ 1, 3, 9, 21649, 64947, 194841, 513239, 1539717, 4619151, 11111111111, 33333333333, 99999999999 ]
Common Lisp
We iterate in the range 1..sqrt(n) collecting ‘low’ factors and corresponding ‘high’ factors, and combine at the end to produce an ordered list of factors.
<lang lisp>(defun factors (n &aux (lows '()) (highs '()))
(do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(remove-duplicates (nreconc lows highs)))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))</lang>
Crystal
Brute force and slow, by checking every value up to n. <lang ruby>struct Int
def factors() (1..self).select { |n| (self % n).zero? } end
end</lang>
Faster, by only checking values up to . <lang ruby>struct Int
def factors
f = [] of Int32
(1..Math.sqrt(self)).each{ |i|
(f << i; f << self // i if self // i != i) if (self % i).zero?
}
f.sort
end
end</lang>
Tests: <lang ruby> [45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}</lang>
- Output:
45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64]
D
Procedural Style
<lang d>import std.stdio, std.math, std.algorithm;
T[] factors(T)(in T n) pure nothrow {
if (n == 1)
return [n];
T[] res = [1, n];
T limit = cast(T)real(n).sqrt + 1;
for (T i = 2; i < limit; i++) {
if (n % i == 0) {
res ~= i;
immutable q = n / i;
if (q > i)
res ~= q;
}
}
return res.sort().release;
}
void main() {
writefln("%(%s\n%)", [45, 53, 64, 1111111].map!factors);
}</lang>
- Output:
[1, 3, 5, 9, 15, 45] [1, 53] [1, 2, 4, 8, 16, 32, 64] [1, 239, 4649, 1111111]
Functional Style
<lang d>import std.stdio, std.algorithm, std.range;
auto factors(I)(I n) {
return iota(1, n + 1).filter!(i => n % i == 0);
}
void main() {
36.factors.writeln;
}</lang>
- Output:
[1, 2, 3, 4, 6, 9, 12, 18, 36]
Dart
import 'dart:math';
factors(n)
{
var factorsArr = [];
factorsArr.add(n);
factorsArr.add(1);
for(var test = n - 1; test >= sqrt(n).toInt(); test--)
if(n % test == 0)
{
factorsArr.add(test);
factorsArr.add(n / test);
}
return factorsArr;
}
void main() {
print(factors(5688));
}
Dc
Simple O(n) version
<lang dc> [Enter positive number: ]P ? sn [Factors of ]P lnn [ are: ]P [q]sq 1si [[ ]P lin]sp [ li ln <q ln li % 0=p li1+si lxx ]dsxx AP </lang>
- Output:
Factors of 998877 are: 1 3 11 33 30269 90807 332959 998877 0m1.120s
Faster O(sqrt(n)) version
<lang dc>
[Enter positive number: ]P ? sn
[Factors of ]P lnn [ are: ]P
[q]sq lnvsv 1si 0sj [[ ]P lin]sp [lkSb lj1+sj]sa [lpx ln li /dsk li<a ]sP
[li lv q lj1-sj Lbsi lpx lxx]dsxx AP
</lang>
0m0.004s
Delphi
See #Pascal.
Dyalect
<lang Dyalect>func Iterator.Where(pred) {
for x in this when pred(x) {
yield x
}
}
func Integer.Factors() {
(1..this).Where(x => this % x == 0)
}
for x in 45.Factors() {
print(x)
}</lang>
Output:
1 3 5 9 15 45
E
<lang e>def factors(x :(int > 0)) {
var xfactors := []
for f ? (x % f <=> 0) in 1..x {
xfactors with= f
}
return xfactors
}</lang>
EasyLang
<lang>n = 720 for i = 1 to n
if n mod i = 0 factors[] &= i .
. print factors[]</lang>
EchoLisp
prime-factors gives the list of n's prime-factors. We mix them to get all the factors. <lang scheme>
- ppows
- input
- a list g of grouped prime factors ( 3 3 3 ..)
- returns (1 3 9 27 ...)
(define (ppows g (mult 1)) (for/fold (ppows '(1)) ((a g)) (set! mult (* mult a)) (cons mult ppows)))
- factors
- decomp n into ((2 2 ..) ( 3 3 ..) ) prime factors groups
- combines (1 2 4 8 ..) (1 3 9 ..) lists
(define (factors n)
(list-sort <
(if (<= n 1) '(1)
(for/fold (divs'(1)) ((g (map ppows (group (prime-factors n)))))
(for*/list ((a divs) (b g)) (* a b)))))) </lang>
- Output:
<lang scheme> (lib 'bigint) (factors 666)
→ (1 2 3 6 9 18 37 74 111 222 333 666)
(length (factors 108233175859200))
→ 666 ;; 💀
(define huge 1200034005600070000008900000000000000000) (time ( length (factors huge)))
→ (394ms 7776)
</lang>
EDSAC order code
Input is limited to 10 decimal digits, which is as many as the EDSAC print subroutine P7 can handle. Factors are printed in pairs, such that the product of the factors in each pair equals the input number.
2021-10-10 Integers are now read from the tape in decimal format, instead of being defined by the awkward method of pseudo-orders. The factorization of 999,999,999 has been removed, as it took too long on the commonly-used EdsacPC simulator (14.6 million orders - over 6 hours on the original EDSAC).
<lang edsac>
[Factors of an integer, from Rosetta Code website.] [EDSAC program, Initial Orders 2.]
[The numbers to be factorized are read in by library subroutine R2
(Wilkes, Wheeler and Gill, 1951 edition, pp.96-97, 148).]
[The address of the integers is placed in location 46, so they can be
referred to by the N parameter (or we could have used 45 and H, etc.)]
T 46 K
P 600 F [address of integers]
[Subroutine R2] GKT20FVDL8FA40DUDTFI40FA40FS39FG@S2FG23FA5@T5@E4@E13Z
T #N [pass address of integers to R2]
[List of integers to be factorized; edit ad lib. R2 requires 'F' after
each integer except the last, and '#' (pi) after the last.
This program uses 0 to mark the end of the list.]
42000F999999F0#
T Z [resume normal loading]
[Modified library subroutine P7.]
[Prints signed integer; up to 10 digits, left-justified.]
[Input: 0D = integer,]
[54 locations. Load at even address. Workspace 4D.]
T 56 K
GKA3FT42@A49@T31@ADE10@T31@A48@T31@SDTDH44#@NDYFLDT4DS43@ TFH17@S17@A43@G23@UFS43@T1FV4DAFG50@SFLDUFXFOFFFSFL4FT4DA49@ T31@A1FA43@G20@XFP1024FP610D@524D!FO46@O26@XFSFL8FT4DE39@
[Division subroutine for positive long integers.
35-bit dividend and divisor (max 2^34 - 1)
returning quotient and remainder.
Input: dividend at 4D, divisor at 6D
Output: remainder at 4D, quotient at 6D.
37 locations; working locations 0D, 8D.]
T 110 K
GKA3FT35@A6DU8DTDA4DRDSDG13@T36@ADLDE4@T36@T6DA4DSDG23@ T4DA6DYFYFT6DT36@A8DSDE35@T36@ADRDTDA6DLDT6DE15@EFPF
[********************** ROSETTA CODE TASK **********************]
[Subroutine to find and print factors of a positive integer.
Input: 0D = integer, maximum 10 decimal digits.
Load at even address.]
T 148 K
G K
A 3 F [form and plant link for return]
T 55 @
A D [load integer whose factors are to be found]
T 56#@ [store]
A 62#@ [load 1]
T 58#@ [possible factor := 1]
S 65 @ [negative count of items per line]
T 64 @ [initialize count]
[Start of loop round possible factors]
[8] T F [clear acc]
A 56#@ [load integer]
T 4 D [to 4F for division]
A 58#@ [load possible factor]
T 6 D [to 6F for division]
A 13 @ [for return from next]
G 110 F [do division; clears acc]
A 6 D [save quotient (6F may be changed below)]
T 60#@
S 4 D [load negative of remainder]
G 44 @ [skip if remainder > 0]
[Here if m is a factor of n.]
[Print m and the quotient together]
T F [clear acc]
A 64 @ [test count of items per line]
G 26 @ [skip if not start of line]
S 65 @ [start of line, reset count]
T 64 @
O 70 @ [and print CR, LF]
O 71 @
[26] T F [clear acc]
O 67 @ [print '(']
A 58#@ [load factor]
T D [to 0D for printing]
A 30 @ [for return from next]
G 56 F [print factor; clears acc]
O 69 @ [print comma]
A 60#@ [load quotient]
T D [to 0D for printing]
A 35 @ [for return from next]
G 56 F [print quotient; clears acc]
O 68 @ [print ')']
A 64 @ [negative counter for items per line]
A 2 F [inc]
E 43 @ [skip if end of line]
O 66 @ [not end of line, print 2 spaces]
O 66 @
[43] T 64 @ [update counter]
[Common code after testing possible factor]
[44] T F [clear acc]
A 58#@ [load possible factor]
A 62#@ [inc by 1]
U 58#@ [store back]
S 60#@ [compare with quotient]
G 8 @ [loop if (new factor) < (old quotient)]
[Here when found all factors]
O 70 @ [print CR, LF twice]
O 71 @
O 70 @
O 71 @
T F [exit with acc = 0]
[55] E F [return]
[--------]
[56] PF PF [number whose factors are to be found]
[58] PF PF [possible factor]
[60] PF PF [integer part of (number/factor)]
T62#Z PF [clear sandwich digit in 35-bit constant 1]
T 62 Z [resume normal loading]
[62] PD PF [35-bit constant 1]
[64] P F [negative counter for items per line]
[65] P 4 F [items per line, in address field]
[66] ! F [space]
[67] K F [left parenthesis (in figures mode)]
[68] L F [right parenthesis (in figures mode)]
[69] N F [comma (in figures mode)]
[70] @ F [carriage return]
[71] & F [line feed]
[Main routine for demonstrating subroutine.]
T 400 K
G K
[0] # F [set figures mode]
[1] K 4096 F [null char]
[2] S #N [order to load negative of first number]
[3] P 2 F [to inc address by 2 for next number]
[Enter with acc = 0]
[4] O @ [set teleprinter to figures]
A 2 @ [load order for first integer]
[6] T 7 @ [plant in next order]
[7] S D [load negative of 35-bit integer]
E 17 @ [exit if number is 0]
T D [negative to 0D]
S D [convert to positive]
T D [pass to subroutine]
A 12 @ [call subroutine to find and print factors]
G 148 F
A 7 @ [modify order above, for next integer]
A 3 @
E 6 @ [always jump, since S = 12 > 0]
[--------]
[17] O 1 @ [done, print null to flush printer buffer]
Z F [stop]
E 4 Z [define entry point]
P F [acc = 0 on entry]
</lang>
- Output:
(1,42000) (2,21000) (3,14000) (4,10500) (5,8400) (6,7000) (7,6000) (8,5250) (10,4200) (12,3500) (14,3000) (15,2800) (16,2625) (20,2100) (21,2000) (24,1750) (25,1680) (28,1500) (30,1400) (35,1200) (40,1050) (42,1000) (48,875) (50,840) (56,750) (60,700) (70,600) (75,560) (80,525) (84,500) (100,420) (105,400) (112,375) (120,350) (125,336) (140,300) (150,280) (168,250) (175,240) (200,210) (1,999999) (3,333333) (7,142857) (9,111111) (11,90909) (13,76923) (21,47619) (27,37037) (33,30303) (37,27027) (39,25641) (63,15873) (77,12987) (91,10989) (99,10101) (111,9009) (117,8547) (143,6993) (189,5291) (231,4329) (259,3861) (273,3663) (297,3367) (333,3003) (351,2849) (407,2457) (429,2331) (481,2079) (693,1443) (777,1287) (819,1221) (999,1001)
Ela
Using higher-order function
<lang ela>open list
factors m = filter (\x -> m % x == 0) [1..m]</lang>
Using comprehension
<lang ela>factors m = [x \\ x <- [1..m] | m % x == 0]</lang>
Elixir
<lang elixir>defmodule RC do
def factor(1), do: [1] def factor(n) do (for i <- 1..div(n,2), rem(n,i)==0, do: i) ++ [n] end # Recursive (faster version); def divisor(n), do: divisor(n, 1, []) |> Enum.sort defp divisor(n, i, factors) when n < i*i , do: factors defp divisor(n, i, factors) when n == i*i , do: [i | factors] defp divisor(n, i, factors) when rem(n,i)==0, do: divisor(n, i+1, [i, div(n,i) | factors]) defp divisor(n, i, factors) , do: divisor(n, i+1, factors)
end
Enum.each([45, 53, 60, 64], fn n ->
IO.puts "#{n}: #{inspect RC.factor(n)}"
end)
IO.puts "\nRange: #{inspect range = 1..10000}" funs = [ factor: &RC.factor/1,
divisor: &RC.divisor/1 ]
Enum.each(funs, fn {name, fun} ->
{time, value} = :timer.tc(fn -> Enum.count(range, &length(fun.(&1))==2) end)
IO.puts "#{name}\t prime count : #{value},\t#{time/1000000} sec"
end) </lang>
- Output:
45: [1, 3, 5, 9, 15, 45] 53: [1, 53] 60: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] 64: [1, 2, 4, 8, 16, 32, 64] Range: 1..10000 factor prime count : 1229, 7.316 sec divisor prime count : 1229, 0.265 sec
Erlang
with Built in fuctions
<lang erlang>factors(N) ->
[I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N].</lang>
Recursive
Another, less concise, but faster version <lang erlang>
-module(divs). -export([divs/1]).
divs(0) -> []; divs(1) -> []; divs(N) -> lists:sort(divisors(1,N))++[N].
divisors(1,N) ->
[1] ++ divisors(2,N,math:sqrt(N)).
divisors(K,_N,Q) when K > Q -> []; divisors(K,N,_Q) when N rem K =/= 0 ->
[] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) when K * K == N ->
[K] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) ->
[K, N div K] ++ divisors(K+1,N,math:sqrt(N)).
</lang>
- Output:
58> timer:tc(divs, factors, [20000]).
{2237,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}
59> timer:tc(divs, divs, [20000]).
{106,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}
The first number is milliseconds. I'v ommitted repeating the first fuction.
ERRE
<lang ERRE> PROGRAM FACTORS
!$DOUBLE
PROCEDURE FACTORLIST(N->L$)
LOCAL C%,I,FLIPS%,I%
LOCAL DIM L[32]
FOR I=1 TO SQR(N) DO
IF N=I*INT(N/I) THEN
L[C%]=I
C%=C%+1
IF N<>I*I THEN
L[C%]=INT(N/I)
C%=C%+1
END IF
END IF
END FOR
! BUBBLE SORT ARRAY L[]
FLIPS%=1
WHILE FLIPS%>0 DO
FLIPS%=0
FOR I%=0 TO C%-2 DO
IF L[I%]>L[I%+1] THEN SWAP(L[I%],L[I%+1]) FLIPS%=1
END FOR
END WHILE
L$=""
FOR I%=0 TO C%-1 DO
L$=L$+STR$(L[I%])+","
END FOR
L$=LEFT$(L$,LEN(L$)-1)
END PROCEDURE
BEGIN
PRINT(CHR$(12);) ! CLS
FACTORLIST(45->L$)
PRINT("The factors of 45 are ";L$)
FACTORLIST(12345->L$)
PRINT("The factors of 12345 are ";L$)
END PROGRAM </lang>
- Output:
The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345
Excel
LAMBDA
Binding the name FACTORS to a custom function defined by the following LAMBDA expression
in the Name Manager of an Excel workbook.
(See: The LAMBDA worksheet function in Excel)
<lang lisp>=LAMBDA(n,
IF(1 < n,
LET(
froot, SQRT(n),
nroot, FLOOR.MATH(froot),
lows, FILTERP(
LAMBDA(x, 0 = MOD(n, x))
)(
ENUMFROMTO(1)(nroot)
),
APPEND(lows)(
LAMBDA(x, n / x)(
REVERSE(
IF(froot <> nroot,
lows,
INIT(lows)
)
)
)
)
),
IF(1 = n, {1}, NA())
)
)</lang>
and assuming that in the same worksheet, each of the following names is bound to the reusable generic lambda expression which follows it:
<lang lisp>APPEND =LAMBDA(xs,
LAMBDA(ys,
LET(
nx, ROWS(xs),
rowIndexes, SEQUENCE(nx + ROWS(ys)),
colIndexes, SEQUENCE(
1,
MAX(COLUMNS(xs), COLUMNS(ys))
),
IF(
rowIndexes <= nx,
INDEX(xs, rowIndexes, colIndexes),
INDEX(ys, rowIndexes - nx, colIndexes)
)
)
)
)
ENUMFROMTO
=LAMBDA(a,
LAMBDA(z,
SEQUENCE(1 + z - a, 1, a, 1)
)
)
FILTERP
=LAMBDA(p,
LAMBDA(xs,
FILTER(xs, p(xs))
)
)
INIT
=LAMBDA(xs,
IF(
AND(1=ROWS(xs), ISBLANK(xs)),
NA(),
INDEX(
xs,
SEQUENCE(ROWS(xs)-1, 1, 1, 1)
)
)
)
REVERSE
=LAMBDA(xs,
LET(
n, ROWS(xs),
SORTBY(
xs,
SEQUENCE(n, 1, n, -1)
)
)
)</lang>
The FACTORS function, applied to an integer, defines a column of integer values.
Here we define a row instead, by composing FACTORS with the standard TRANSPOSE function.
- Output:
| fx | =TRANSPOSE(FACTORS(A2)) | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | ||
| 1 | N | Factors | ||||||||||||||||
| 2 | 64 | 1 | 2 | 4 | 8 | 16 | 32 | 64 | ||||||||||
| 3 | 120 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | |
| 4 | 123456789 | 1 | 3 | 9 | 3607 | 3803 | 10821 | 11409 | 32463 | 34227 | 13717421 | 41152263 | 123456789 | |||||
| 5 | 2 | 1 | 2 | |||||||||||||||
| 6 | 1 | 1 | ||||||||||||||||
| 7 | 0 | #N/A | ||||||||||||||||
| 8 | -1 | #N/A | ||||||||||||||||
F#
If number % divisor = 0 then both divisor AND number / divisor are factors.
So, we only have to search till sqrt(number).
Also, this is lazily evaluated. <lang fsharp>let factors number = seq {
for divisor in 1 .. (float >> sqrt >> int) number do
if number % divisor = 0 then
yield divisor
if number <> 1 then yield number / divisor //special case condition: when number=1 then divisor=(number/divisor), so don't repeat it
}</lang>
Prime factoring
<lang fsharp> [6;120;2048;402642;1206432] |> Seq.iter(fun n->printf "%d :" n; [1..n]|>Seq.filter(fun g->n%g=0)|>Seq.iter(fun n->printf " %d" n); printfn "");;</lang>
- Output:
OUTPUT : 6 : 1 2 3 6 120 : 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 2048 : 1 2 4 8 16 32 64 128 256 512 1024 2048 402642 : 1 2 3 6 9 18 22369 44738 67107 134214 201321 402642 120643200 : 1 2 3 4 6 8 9 12 16 18 24 32 36 48 59 71 72 96 118 142 144 177 213 236 284 288 354 426 472 531 568 639 708 852 944 1062 1136 12 78 1416 1704 1888 2124 2272 2556 2832 3408 4189 4248 5112 5664 6816 8378 8496 10224 12567 16756 16992 20448 25134 33512 37701 50268 67024 75402 10053 6 134048 150804 201072 301608 402144 603216 1206432
Factor
USE: math.primes.factors
( scratchpad ) 24 divisors .
{ 1 2 3 4 6 8 12 24 }
FALSE
<lang false>[1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f: 45f;! 53f;! 64f;!</lang>
Fish
<lang Fish>0v
>i:0(?v'0'%+a*
>~a,:1:>r{% ?vr:nr','ov
^:&:;?(&:+1r:< <
</lang> Must be called with pre-polulated value (Positive Integer) in the input stack. Try at Fish Playground[1].
For Input Number :
120
The following output was generated:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120,
Forth
This is a slightly optimized algorithm, since it realizes there are no factors between n/2 and n. The values are saved on the stack and - in true Forth fashion - printed in descending order. <lang Forth>: factors dup 2/ 1+ 1 do dup i mod 0= if i swap then loop ;
- .factors factors begin dup dup . 1 <> while drop repeat drop cr ;
45 .factors 53 .factors 64 .factors 100 .factors</lang>
Alternative version with vectored execution
It's not really idiomatic FORTH to leave a variable number of items on the stack, so instead this version repeatedly calls an execution token for each factor, and it uses a defining word to create a fold over the factors of an integer. This version also only tests up to the square root, which means that items are generated in pairs, rather than in sorted order. <lang FORTH>
- sq s" dup *" evaluate ; immediate
- factors ( n a xt -- )
swap 2>r 1
BEGIN 2dup sq > WHILE
2dup /mod swap 0= IF
over
r> r@ execute
r@ execute >r
ELSE
drop
THEN 1+
REPEAT
2dup sq = IF
2r> swap execute nip
ELSE
2drop r> rdrop
THEN ;
- <with-factors>
create 2, does> 2@ factors ;
0 :noname nip 1+ ; <with-factors> count-factors 0 ' + <with-factors> sum-factors
0 :noname swap . ; <with-factors> (.factors)
- .factors (.factors) drop ;
</lang>
- Output:
100 .factors 1 100 2 50 4 25 5 20 10 ok 100 count-factors . 9 ok 100 sum-factors . 217 ok 1 100 + 2 + 50 + 4 + 25 + 5 + 20 + 10 + . 217 ok \ test sum-factors result 77 .factors 1 77 7 11 ok 108 .factors 1 108 2 54 3 36 4 27 6 18 9 12 ok
Fortran
<lang fortran>program Factors
implicit none integer :: i, number write(*,*) "Enter a number between 1 and 2147483647" read*, number
do i = 1, int(sqrt(real(number))) - 1
if (mod(number, i) == 0) write (*,*) i, number/i
end do
! Check to see if number is a square
i = int(sqrt(real(number)))
if (i*i == number) then
write (*,*) i
else if (mod(number, i) == 0) then
write (*,*) i, number/i
end if
end program</lang>
FreeBASIC
<lang freebasic>' FB 1.05.0 Win64
Sub printFactors(n As Integer)
If n < 1 Then Return Print n; " =>"; For i As Integer = 1 To n / 2 If n Mod i = 0 Then Print i; " "; Next i Print n
End Sub
printFactors(11) printFactors(21) printFactors(32) printFactors(45) printFactors(67) printFactors(96) Print Print "Press any key to quit" Sleep</lang>
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
Frink
Frink has built-in factoring functions which use wheel factoring, trial division, Pollard p-1 factoring, and Pollard rho factoring. It also recognizes some special forms (e.g. Mersenne numbers) and handles them efficiently. Integers can either be decomposed into prime factors or all factors.
The factors[n] function will return the prime decomposition of n.
The allFactors[n, include1=true, includeN=true, sort=true, onlyToSqrt=false] function will return all factors of n. The optional arguments include1 and includeN indicate if the numbers 1 and n are to be included in the results. If the optional argument sort is true, the results will be sorted. If the optional argument onlyToSqrt=true, then only the factors less than or equal to the square root of the number will be produced.
The following produces all factors of n, including 1 and n:
<lang frink>allFactors[n]</lang>
FunL
Function to compute set of factors: <lang funl>def factors( n ) = {d | d <- 1..n if d|n}</lang>
Test: <lang funl>for x <- [103, 316, 519, 639, 760]
println( 'The set of factors of ' + x + ' is ' + factors(x) )</lang>
- Output:
The set of factors of 103 is {1, 103}
The set of factors of 316 is {158, 4, 79, 1, 2, 316}
The set of factors of 519 is {1, 3, 173, 519}
The set of factors of 639 is {9, 639, 71, 213, 1, 3}
The set of factors of 760 is {8, 19, 4, 40, 152, 5, 10, 76, 1, 95, 190, 760, 20, 2, 38, 380}
FutureBasic
<lang futurebasic> include "ConsoleWindow"
clear local mode local fn IntegerFactors( f as long ) as Str255 dim as long i, s, l(100), c : c = 0 dim as Str255 factorStr
for i = 1 to sqr(f)
if ( f mod i == 0 )
l(c) = i
c++
if ( f <> i ^ 2 )
l(c) = ( f / i )
c++
end if
end if
next i s = 1 while ( s = 1 ) s = 0
for i = 0 to c-1
if l(i) > l(i+1) and l(i+1) <> 0
swap l(i), l(i+1)
s = 1
end if
next i
wend for i = 0 to c-1
if ( i < c -1 ) factorStr = factorStr + str$(l(i)) + "," else factorStr = factorStr + str$(l(i)) end if
next end fn = factorStr
print "Factors of 25 are:"; fn IntegerFactors( 25 ) print "Factors of 45 are:"; fn IntegerFactors( 45 ) print "Factors of 103 are:"; fn IntegerFactors( 103 ) print "Factors of 760 are:"; fn IntegerFactors( 760 ) print "Factors of 12345 are:"; fn IntegerFactors( 12345 ) print "Factors of 32766 are:"; fn IntegerFactors( 32766 ) print "Factors of 32767 are:"; fn IntegerFactors( 32767 ) print "Factors of 57097 are:"; fn IntegerFactors( 57097 ) print "Factors of 12345678 are:"; fn IntegerFactors( 12345678 ) print "Factors of 32434243 are:"; fn IntegerFactors( 32434243 ) </lang>
Output:
Factors of 25 are: 1, 5, 25 Factors of 45 are: 1, 3, 5, 9, 15, 45 Factors of 103 are: 1, 103 Factors of 760 are: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 Factors of 12345 are: 1, 3, 5, 15, 823, 2469, 4115, 12345 Factors of 32766 are: 1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766 Factors of 32767 are: 1, 7, 31, 151, 217, 1057, 4681, 32767 Factors of 57097 are: 1, 57097 Factors of 12345678 are: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779, 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839, 12345678 Factors of 32434243 are: 1, 307, 105649, 32434243
GAP
<lang gap># Built-in function DivisorsInt(Factorial(5));
- [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
- A possible implementation, not suitable to large n
div := n -> Filtered([1 .. n], k -> n mod k = 0);
div(Factorial(5));
- [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
- Another implementation, usable for large n (if n can be factored quickly)
div2 := function(n)
local f, p; f := Collected(FactorsInt(n)); p := List(f, v -> List([0 .. v[2]], k -> v[1]^k)); return SortedList(List(Cartesian(p), Product));
end;
div2(Factorial(5));
- [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]</lang>
Go
Trial division, no prime number generator, but with some optimizations. It's good enough to factor any 64 bit integer, with large primes taking several seconds. <lang go>package main
import "fmt"
func main() {
printFactors(-1) printFactors(0) printFactors(1) printFactors(2) printFactors(3) printFactors(53) printFactors(45) printFactors(64) printFactors(600851475143) printFactors(999999999999999989)
}
func printFactors(nr int64) {
if nr < 1 {
fmt.Println("\nFactors of", nr, "not computed")
return
}
fmt.Printf("\nFactors of %d: ", nr)
fs := make([]int64, 1)
fs[0] = 1
apf := func(p int64, e int) {
n := len(fs)
for i, pp := 0, p; i < e; i, pp = i+1, pp*p {
for j := 0; j < n; j++ {
fs = append(fs, fs[j]*pp)
}
}
}
e := 0
for ; nr & 1 == 0; e++ {
nr >>= 1
}
apf(2, e)
for d := int64(3); nr > 1; d += 2 {
if d*d > nr {
d = nr
}
for e = 0; nr%d == 0; e++ {
nr /= d
}
if e > 0 {
apf(d, e)
}
}
fmt.Println(fs)
fmt.Println("Number of factors =", len(fs))
}</lang>
- Output:
Factors of -1 not computed Factors of 0 not computed Factors of 1: [1] Number of factors = 1 Factors of 2: [1 2] Number of factors = 2 Factors of 3: [1 3] Number of factors = 2 Factors of 53: [1 53] Number of factors = 2 Factors of 45: [1 3 9 5 15 45] Number of factors = 6 Factors of 64: [1 2 4 8 16 32 64] Number of factors = 7 Factors of 600851475143: [1 71 839 59569 1471 104441 1234169 87625999 6857 486847 5753023 408464633 10086647 716151937 8462696833 600851475143] Number of factors = 16 Factors of 999999999999999989: [1 999999999999999989] Number of factors = 2
Gosu
<lang gosu>var numbers = {11, 21, 32, 45, 67, 96} numbers.each(\ number -> printFactors(number))
function printFactors(n: int) {
if (n < 1) return
var result ="${n} => "
(1 .. n/2).each(\ i -> {result += n % i == 0 ? "${i} " : ""})
print("${result}${n}")
}</lang>
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
Groovy
A straight brute force approach up to the square root of N: <lang groovy>def factorize = { long target ->
if (target == 1) return [1L]
if (target < 4) return [1L, target]
def targetSqrt = Math.sqrt(target)
def lowfactors = (2L..targetSqrt).grep { (target % it) == 0 }
if (lowfactors == []) return [1L, target]
def nhalf = lowfactors.size() - ((lowfactors[-1] == targetSqrt) ? 1 : 0)
[1] + lowfactors + (0..<nhalf).collect { target.intdiv(lowfactors[it]) }.reverse() + [target]
}</lang>
Test: <lang groovy>((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) }</lang>
- Output:
[number:1, factors:[1]] [number:2, factors:[1, 2]] [number:3, factors:[1, 3]] [number:4, factors:[1, 2, 4]] [number:5, factors:[1, 5]] [number:6, factors:[1, 2, 3, 6]] [number:7, factors:[1, 7]] [number:8, factors:[1, 2, 4, 8]] [number:9, factors:[1, 3, 9]] [number:10, factors:[1, 2, 5, 10]] [number:11, factors:[1, 11]] [number:12, factors:[1, 2, 3, 4, 6, 12]] [number:13, factors:[1, 13]] [number:14, factors:[1, 2, 7, 14]] [number:15, factors:[1, 3, 5, 15]] [number:16, factors:[1, 2, 4, 8, 16]] [number:17, factors:[1, 17]] [number:18, factors:[1, 2, 3, 6, 9, 18]] [number:19, factors:[1, 19]] [number:20, factors:[1, 2, 4, 5, 10, 20]] [number:21, factors:[1, 3, 7, 21]] [number:22, factors:[1, 2, 11, 22]] [number:23, factors:[1, 23]] [number:24, factors:[1, 2, 3, 4, 6, 8, 12, 24]] [number:25, factors:[1, 5, 25]] [number:26, factors:[1, 2, 13, 26]] [number:27, factors:[1, 3, 9, 27]] [number:28, factors:[1, 2, 4, 7, 14, 28]] [number:29, factors:[1, 29]] [number:30, factors:[1, 2, 3, 5, 6, 10, 15, 30]] [number:333333, factors:[1, 3, 7, 9, 11, 13, 21, 33, 37, 39, 63, 77, 91, 99, 111, 117, 143, 231, 259, 273, 333, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2331, 2849, 3003, 3367, 3663, 4329, 5291, 8547, 9009, 10101, 15873, 25641, 30303, 37037, 47619, 111111, 333333]]
Haskell
Using D. Amos'es Primes module for finding prime factors <lang Haskell>import HFM.Primes (primePowerFactors) import Control.Monad (mapM) import Data.List (product)
-- primePowerFactors :: Integer -> [(Integer,Int)]
factors = map product .
mapM (\(p,m)-> [p^i | i<-[0..m]]) . primePowerFactors</lang>
Returns list of factors out of order, e.g.:
<Lang haskell>~> factors 42 [1,7,3,21,2,14,6,42]</lang>
Or, prime decomposition task can be used (although, a trial division-only version will become very slow for large primes),
<lang haskell>import Data.List (group) primePowerFactors = map (\x-> (head x, length x)) . group . factorize</lang>
The above function can also be found in the package arithmoi, as Math.NumberTheory.Primes.factorise :: Integer -> [(Integer, Int)], which performs "factorisation of Integers by the elliptic curve algorithm after Montgomery" and "is best suited for numbers of up to 50-60 digits".
Or, deriving cofactors from factors up to the square root:
<lang Haskell>integerFactors :: Int -> [Int] integerFactors n
| 1 > n = []
| otherwise = lows ++ fmap (quot n) (part n (reverse lows))
where
part n
| n == square = tail
| otherwise = id
(square, lows) =
(,) . (^ 2) <*> (filter ((0 ==) . rem n) . enumFromTo 1) $
floor (sqrt $ fromIntegral n)
main :: IO () main = print $ integerFactors 600</lang>
- Output:
[1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600]
List comprehension
Naive, functional, no import, in increasing order: <lang Haskell>factorsNaive n =
[ i | i <- [1 .. n] , mod n i == 0 ]</lang>
<lang Haskell>~> factorsNaive 25 [1,5,25]</lang>
Factor, cofactor. Get the list of factor–cofactor pairs sorted, for a quadratic speedup: <lang Haskell>import Data.List (sort)
factorsCo n =
sort
[ i
| i <- [1 .. floor (sqrt (fromIntegral n))]
, (d, 0) <- [divMod n i]
, i <-
i :
[ d
| d > i ] ]</lang>
A version of the above without the need for sorting, making it to be online (i.e. productive immediately, which can be seen in GHCi); factors in increasing order: <lang Haskell>factorsO n =
ds ++
[ r
| (d, 0) <- [divMod n r]
, r <-
r :
[ d
| d > r ] ] ++
reverse (map (n `div`) ds)
where
r = floor (sqrt (fromIntegral n))
ds =
[ i
| i <- [1 .. r - 1]
, mod n i == 0 ]</lang>
Testing: <lang Haskell>*Main> :set +s ~> factorsO 120 [1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120] (0.00 secs, 0 bytes)
~> factorsO 12041111117 [1,7,41,287,541,3787,22181,77551,155267,542857,3179591,22257137,41955091,2936856 37,1720158731,12041111117] (0.09 secs, 50758224 bytes)</lang>
HicEst
<lang hicest> DLG(NameEdit=N, TItle='Enter an integer')
DO i = 1, N^0.5 IF( MOD(N,i) == 0) WRITE() i, N/i ENDDO
END</lang>
Icon and Unicon
<lang Icon>procedure main(arglist) numbers := arglist ||| [ 32767, 45, 53, 64, 100] # combine command line provided and default set of values every writes(lf,"factors of ",i := !numbers,"=") & writes(divisors(i)," ") do lf := "\n" end
link factors</lang>
- Output:
factors of 32767=1 7 31 151 217 1057 4681 32767 factors of 45=1 3 5 9 15 45 factors of 53=1 53 factors of 64=1 2 4 8 16 32 64 factors of 100=1 2 4 5 10 20 25 50 100
J
The "brute force" approach is the most concise:
<lang J>foi=: [: I. 0 = (|~ i.@>:)</lang>
Example use:
<lang J> foi 40 1 2 4 5 8 10 20 40</lang>
Basically we test every non-negative integer up through the number itself to see if it divides evenly.
However, this becomes very slow for large numbers. So other approaches can be worthwhile.
J has a primitive, q: which returns its argument's prime factors. <lang J>q: 40
2 2 2 5</lang>
Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors <lang J> __ q: 420 2 3 5 7 2 1 1 1</lang>
With this, we can form lists of each of the potential relevant powers of each of these prime factors <lang J> (^ i.@>:)&.>/ __ q: 420 ┌─────┬───┬───┬───┐ │1 2 4│1 3│1 5│1 7│ └─────┴───┴───┴───┘</lang>
From here, it's a simple matter (*/&>@{ or, find all possible combinations of one item from each list ({ without a left argument) then unpack each list and multiply its elements) to compute all possible factors of the original number
<lang J>factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__
factrs 40 1 5 2 10 4 20 8 40</lang>
However, a data structure which is organized around the prime decomposition of the argument can be hard to read. So, for reader convenience, we should probably arrange them in a monotonically increasing list:
<lang J> factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__
factors 420
1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420</lang>
A less efficient, but concise variation on this theme:
<lang J> ~.,*/&> { 1 ,&.> q: 40 1 5 2 10 4 20 8 40</lang>
This computes 2^n intermediate values where n is the number of prime factors of the original number.
That said, note that we get a representation issue when dealing with large numbers:
<lang J> factors 568474220 1 2 4 5 10 17 20 34 68 85 170 340 1.67198e6 3.34397e6 6.68793e6 8.35992e6 1.67198e7 2.84237e7 3.34397e7 5.68474e7 1.13695e8 1.42119e8 2.84237e8 5.68474e8</lang>
One approach here (if we don't want to explicitly format the result) is to use an arbitrary precision (aka "extended") argument. This propagates through into the result:
<lang J> factors 568474220x 1 2 4 5 10 17 20 34 68 85 170 340 1671983 3343966 6687932 8359915 16719830 28423711 33439660 56847422 113694844 142118555 284237110 568474220</lang>
Another less efficient approach, in which remainders are examined up to the square root, larger factors obtained as fractions, and the combined list nubbed and sorted might be: <lang J>factorsOfNumber=: monad define
Y=. y"_ /:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y
)
factorsOfNumber 40
1 2 4 5 8 10 20 40</lang>
Another approach:
<lang J>odometer =: #: i.@(*/) factors=: (*/@:^"1 odometer@:>:)/@q:~&__</lang>
See http://www.jsoftware.com/jwiki/Essays/Odometer
Java
<lang java5>public static TreeSet<Long> factors(long n) {
TreeSet<Long> factors = new TreeSet<Long>();
factors.add(n);
factors.add(1L);
for(long test = n - 1; test >= Math.sqrt(n); test--)
if(n % test == 0)
{
factors.add(test);
factors.add(n / test);
}
return factors;
}</lang>
JavaScript
Imperative
<lang javascript>function factors(num) {
var n_factors = [], i;
for (i = 1; i <= Math.floor(Math.sqrt(num)); i += 1)
if (num % i === 0)
{
n_factors.push(i);
if (num / i !== i)
n_factors.push(num / i);
}
n_factors.sort(function(a, b){return a - b;}); // numeric sort
return n_factors;
}
factors(45); // [1,3,5,9,15,45] factors(53); // [1,53] factors(64); // [1,2,4,8,16,32,64]</lang>
Functional
ES5
Translating the naive list comprehension example from Haskell, using a list monad for the comprehension
<lang JavaScript>// Monadic bind (chain) for lists function chain(xs, f) {
return [].concat.apply([], xs.map(f));
}
// [m..n] function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
function factors_naive(n) {
return chain( range(1, n), function (x) { // monadic chain/bind
return n % x ? [] : [x]; // monadic fail or inject/return
});
}
factors_naive(6)</lang>
Output: <lang JavaScript>[1, 2, 3, 6]</lang>
Translating the Haskell (lows and highs) example
<lang JavaScript>console.log(
(function (lstTest) {
// INTEGER FACTORS
function integerFactors(n) {
var rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
lows = range(1, intRoot).filter(function (x) {
return (n % x) === 0;
});
// for perfect squares, we can drop the head of the 'highs' list
return lows.concat(lows.map(function (x) {
return n / x;
}).reverse().slice((rRoot === intRoot) | 0));
}
// [m .. n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
/*************************** TESTING *****************************/
// TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS
function alignedTable(lstRows, lngPad, fnAligned) {
var lstColWidths = range(0, lstRows.reduce(function (a, x) {
return x.length > a ? x.length : a;
}, 0) - 1).map(function (iCol) {
return lstRows.reduce(function (a, lst) {
var w = lst[iCol] ? lst[iCol].toString().length : 0;
return (w > a) ? w : a;
}, 0);
});
return lstRows.map(function (lstRow) {
return lstRow.map(function (v, i) {
return fnAligned(v, lstColWidths[i] + lngPad);
}).join()
}).join('\n');
}
function alignRight(n, lngWidth) {
var s = n.toString();
return Array(lngWidth - s.length + 1).join(' ') + s;
}
// TEST
return '\nintegerFactors(n)\n\n' + alignedTable(
lstTest.map(integerFactors).map(function (x, i) {
return [lstTest[i], '-->'].concat(x);
}), 2, alignRight
) + '\n';
})([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767])
);</lang>
Output:
<lang JavaScript>integerFactors(n)
25 --> 1 5 25
45 --> 1 3 5 9 15 45
53 --> 1 53
64 --> 1 2 4 8 16 32 64
100 --> 1 2 4 5 10 20 25 50 100
102 --> 1 2 3 6 17 34 51 102
120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
12345 --> 1 3 5 15 823 2469 4115 12345
32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
32767 --> 1 7 31 151 217 1057 4681 32767
</lang>
ES6
<lang JavaScript>(function (lstTest) {
'use strict';
// INTEGER FACTORS
// integerFactors :: Int -> [Int]
let integerFactors = (n) => {
let rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
lows = range(1, intRoot)
.filter(x => (n % x) === 0);
// for perfect squares, we can drop
// the head of the 'highs' list
return lows.concat(lows
.map(x => n / x)
.reverse()
.slice((rRoot === intRoot) | 0)
);
},
// range :: Int -> Int -> [Int]
range = (m, n) => Array.from({
length: (n - m) + 1
}, (_, i) => m + i);
/*************************** TESTING *****************************/
// TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS
let alignedTable = (lstRows, lngPad, fnAligned) => {
var lstColWidths = range(
0, lstRows
.reduce(
(a, x) => (x.length > a ? x.length : a),
0
) - 1
)
.map((iCol) => lstRows
.reduce((a, lst) => {
let w = lst[iCol] ? lst[iCol].toString()
.length : 0;
return (w > a) ? w : a;
}, 0));
return lstRows.map((lstRow) =>
lstRow.map((v, i) => fnAligned(
v, lstColWidths[i] + lngPad
))
.join()
)
.join('\n');
},
alignRight = (n, lngWidth) => {
let s = n.toString();
return Array(lngWidth - s.length + 1)
.join(' ') + s;
};
// TEST
return '\nintegerFactors(n)\n\n' + alignedTable(lstTest
.map(integerFactors)
.map(
(x, i) => [lstTest[i], '-->'].concat(x)
), 2, alignRight
) + '\n';
})([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]);</lang>
- Output:
integerFactors(n)
25 --> 1 5 25
45 --> 1 3 5 9 15 45
53 --> 1 53
64 --> 1 2 4 8 16 32 64
100 --> 1 2 4 5 10 20 25 50 100
102 --> 1 2 3 6 17 34 51 102
120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
12345 --> 1 3 5 15 823 2469 4115 12345
32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
32767 --> 1 7 31 151 217 1057 4681 32767
jq
<lang jq># This implementation uses "sort" for tidiness def factors:
. as $num
| reduce range(1; 1 + sqrt|floor) as $i
([];
if ($num % $i) == 0 then
($num / $i) as $r
| if $i == $r then . + [$i] else . + [$i, $r] end
else .
end )
| sort;
def task:
(45, 53, 64) | "\(.): \(factors)" ;
task</lang>
- Output:
$ jq -n -M -r -c -f factors.jq 45: [1,3,5,9,15,45] 53: [1,53] 64: [1,2,4,8,16,32,64]
Julia
<lang julia>using Primes
function factors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, [f*p^j for j in 1:e], init=f)
end
return length(f) == 1 ? [one(n), n] : sort!(f)
end
const examples = [28, 45, 53, 64, 6435789435768]
for n in examples
@time println("The factors of $n are: $(factors(n))")
end </lang>
- Output:
The factors of 28 are: [1, 2, 4, 7, 14, 28] 0.330684 seconds (784.75 k allocations: 39.104 MiB, 3.17% gc time) The factors of 45 are: [1, 3, 5, 9, 15, 45] 0.000117 seconds (56 allocations: 2.672 KiB) The factors of 53 are: [1, 53] 0.000102 seconds (35 allocations: 1.516 KiB) The factors of 64 are: [1, 2, 4, 8, 16, 32, 64] 0.000093 seconds (56 allocations: 3.172 KiB) The factors of 6435789435768 are: [1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 191, 231, 264, 308, 382, 462, 573, 616, 764, 924, 1146, 1337, 1528, 1848, 2101, 2292, 2674, 4011, 4202, 4584, 5348, 6303, 8022, 8404, 10696, 12606, 14707, 16044, 16808, 25212, 29414, 32088, 44121, 50424, 58828, 88242, 117656, 176484, 352968, 18233351, 36466702, 54700053, 72933404, 109400106, 127633457, 145866808, 200566861, 218800212, 255266914, 382900371, 401133722, 437600424, 510533828, 601700583, 765800742, 802267444, 1021067656, 1203401166, 1403968027, 1531601484, 1604534888, 2406802332, 2807936054, 3063202968, 3482570041, 4211904081, 4813604664, 5615872108, 6965140082, 8423808162, 10447710123, 11231744216, 13930280164, 16847616324, 20895420246, 24377990287, 27860560328, 33695232648, 38308270451, 41790840492, 48755980574, 73133970861, 76616540902, 83581680984, 97511961148, 114924811353, 146267941722, 153233081804, 195023922296, 229849622706, 268157893157, 292535883444, 306466163608, 459699245412, 536315786314, 585071766888, 804473679471, 919398490824, 1072631572628, 1608947358942, 2145263145256, 3217894717884, 6435789435768] 0.000249 seconds (451 allocations: 24.813 KiB)
K
<lang K> f:{i:{y[&x=y*x div y]}[x;1+!_sqrt x];?i,x div|i} equivalent to: q)f:{i:{y where x=y*x div y}[x ; 1+ til floor sqrt x]; distinct i,x div reverse i}
f 120
1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
f 1024
1 2 4 8 16 32 64 128 256 512 1024
f 600851475143
1 71 839 1471 6857 59569 104441 486847 1234169 5753023 10086647 87625999 408464633 716151937 8462696833 600851475143
#f 3491888400 / has 1920 factors
1920
/ Number of factors for 3491888400 .. 3491888409 #:'f' 3491888400+!10
1920 16 4 4 12 16 32 16 8 24</lang>
Kotlin
<lang scala>fun printFactors(n: Int) {
if (n < 1) return
print("$n => ")
(1..n / 2)
.filter { n % it == 0 }
.forEach { print("$it ") }
println(n)
}
fun main(args: Array<String>) {
val numbers = intArrayOf(11, 21, 32, 45, 67, 96) for (number in numbers) printFactors(number)
}</lang>
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
Lambdatalk
<lang scheme> {def factors
{def factors.r
{lambda {:num :i :N}
{if {> :i :N}
then
else {if {= {% :num :i} 0}
then :i
{if {not {= {/ :num :i} :i}}
then {/ :num :i}
else}
else}
{factors.r :num {+ :i 1} :N} }}}
{lambda {:n}
{S.sort < {factors.r :n 1 {sqrt :n}}}}}
-> factors
{factors 45} -> 1 3 5 9 15 45 {factors 53} -> 1 53 {factors 64} -> 1 2 4 8 16 32 64
</lang>
LFE
Using List Comprehensions
This following function is elegant looking and concise. However, it will not handle large numbers well: it will consume a great deal of memory (on one large number, the function consumed 4.3GB of memory on my desktop machine): <lang lisp> (defun factors (n)
(list-comp ((<- i (when (== 0 (rem n i))) (lists:seq 1 (trunc (/ n 2))))) i))
</lang>
Non-Stack-Consuming
This version will not consume the stack (this function only used 18MB of memory on my machine with a ridiculously large number): <lang lisp> (defun factors (n)
"Tail-recursive prime factors function." (factors n 2 '()))
(defun factors
((1 _ acc) (++ acc '(1))) ((n _ acc) (when (=< n 0)) #(error undefined)) ((n k acc) (when (== 0 (rem n k))) (factors (div n k) k (cons k acc))) ((n k acc) (factors n (+ k 1) acc)))
</lang>
- Output:
> (factors 10677106534462215678539721403561279) (104729 104729 104729 98731 98731 32579 29269 1)
Liberty BASIC
<lang lb>num = 10677106534462215678539721403561279 maxnFactors = 1000 dim primeFactors(maxnFactors), nPrimeFactors(maxnFactors) global nDifferentPrimeNumbersFound, nFactors, iFactor
print "Start finding all factors of ";num; ":"
nDifferentPrimeNumbersFound=0 dummy = factorize(num,2) nFactors = showPrimeFactors(num) dim factors(nFactors) dummy = generateFactors(1,1) sort factors(), 0, nFactors-1 for i=1 to nFactors
print i;" ";factors(i-1)
next i
print "done"
wait
function factorize(iNum,offset)
factorFound=0
i = offset
do
if (iNum MOD i)=0 _
then
if primeFactors(nDifferentPrimeNumbersFound) = i _
then
nPrimeFactors(nDifferentPrimeNumbersFound) = nPrimeFactors(nDifferentPrimeNumbersFound) + 1
else
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = i
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
if iNum/i<>1 then dummy = factorize(iNum/i,i)
factorFound=1
end if
i=i+1
loop while factorFound=0 and i<=sqr(iNum)
if factorFound=0 _
then
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = iNum
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
end function
function showPrimeFactors(iNum)
showPrimeFactors=1
print iNum;" = ";
for i=1 to nDifferentPrimeNumbersFound
print primeFactors(i);"^";nPrimeFactors(i);
if i<nDifferentPrimeNumbersFound then print " * "; else print ""
showPrimeFactors = showPrimeFactors*(nPrimeFactors(i)+1)
next i
end function
function generateFactors(product,pIndex)
if pIndex>nDifferentPrimeNumbersFound _
then
factors(iFactor) = product
iFactor=iFactor+1
else
for i=0 to nPrimeFactors(pIndex)
dummy = generateFactors(product*primeFactors(pIndex)^i,pIndex+1)
next i
end if
end function</lang>
- Output:
<lang lb>Start finding all factors of 10677106534462215678539721403561279: 10677106534462215678539721403561279 = 29269^1 * 32579^1 * 98731^2 * 104729^3 1 1 2 29269 3 32579 4 98731 5 104729 6 953554751 7 2889757639 8 3065313101 9 3216557249 10 3411966091 11 9747810361 12 10339998899 13 10968163441 14 94145414120981 15 99864835517479 16 285308661456109 17 302641427774831 18 317573913751019 19 321027175754629 20 336866824130521 21 357331796744339 22 1020878431297169 23 1082897744693371 24 1148684789012489 25 9295070881578575111 26 9859755075476219149 27 10458744358910058191 28 29880090805636839461 29 31695334089430275799 30 33259198413230468851 31 33620855089606540541 32 35279725624365333809 33 37423001741237879131 34 106915577231321212201 35 113410797903992051459 36 973463478356842592799919 37 1032602289299548955255621 38 1095333837964291484285239 39 3129312029983540559911069 40 3319420643851943354153471 41 3483202590619213772296379 42 3694810384914157044482761 43 11197161487859039232598529 44 101949856624833767901342716951 45 108143405156052462534965931709 46 327729719588146219298926345301 47 364792324112959639158827476291 48 10677106534462215678539721403561279 done</lang>
A Simpler Approach
This is a somewhat simpler approach for finding the factors of smaller numbers (less than one million).
<lang lb> print "ROSETTA CODE - Factors of an integer" 'A simpler approach for smaller numbers [Start] print input "Enter an integer (< 1,000,000): "; n n=abs(int(n)): if n=0 then goto [Quit] if n>999999 then goto [Start] FactorCount=FactorCount(n) select case FactorCount
case 1: print "The factor of 1 is: 1"
case else
print "The "; FactorCount; " factors of "; n; " are: ";
for x=1 to FactorCount
print " "; Factor(x);
next x
if FactorCount=2 then print " (Prime)" else print
end select goto [Start]
[Quit] print "Program complete." end
function FactorCount(n)
dim Factor(100)
for y=1 to n
if y>sqr(n) and FactorCount=1 then
'If no second factor is found by the square root of n, then n is prime.
FactorCount=2: Factor(FactorCount)=n: exit function
end if
if (n mod y)=0 then
FactorCount=FactorCount+1
Factor(FactorCount)=y
end if
next y
end function </lang>
- Output:
ROSETTA CODE - Factors of an integer Enter an integer (< 1,000,000): 1 The factor of 1 is: 1 Enter an integer (< 1,000,000): 2 The 2 factors of 2 are: 1 2 (Prime) Enter an integer (< 1,000,000): 4 The 3 factors of 4 are: 1 2 4 Enter an integer (< 1,000,000): 6 The 4 factors of 6 are: 1 2 3 6 Enter an integer (< 1,000,000): 999999 The 64 factors of 999999 are: 1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 111 117 143 189 231 259 273 297 333 351 407 429 481 693 777 819 999 1001 1221 1287 1443 2079 2331 2457 2849 3003 3367 3663 3861 4329 5291 6993 8547 9009 10101 10989 129 87 15873 25641 27027 30303 37037 47619 76923 90909 111111 142857 333333 999999 Enter an integer (< 1,000,000): Program complete.
Lingo
<lang lingo>on factors(n)
res = [1] repeat with i = 2 to n/2 if n mod i = 0 then res.add(i) end repeat res.add(n) return res
end</lang> <lang lingo>put factors(45) -- [1, 3, 5, 9, 15, 45] put factors(53) -- [1, 53] put factors(64) -- [1, 2, 4, 8, 16, 32, 64]</lang>
Logo
<lang logo>to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end
show factors 28 ; [1 2 4 7 14 28]</lang>
Lua
<lang lua>function Factors( n )
local f = {}
for i = 1, n/2 do
if n % i == 0 then
f[#f+1] = i
end
end
f[#f+1] = n
return f
end</lang>
M2000 Interpreter
<lang M2000 Interpreter> \\ Factors of an integer \\ For act as BASIC's FOR (if N<1 no loop start) FORM 60,40 SET SWITCHES "+FOR" MODULE LikeBasic {
10 INPUT N%
20 FOR I%=1 TO N%
30 IF N%/I%=INT(N%/I%) THEN PRINT I%,
40 NEXT I%
50 PRINT
} CALL LikeBasic SET SWITCHES "-FOR" MODULE LikeM2000 {
DEF DECIMAL N%, I%
INPUT N%
IF N%<1 THEN EXIT
FOR I%=1 TO N% {
IF N% MOD I%=0 THEN PRINT I%,
}
PRINT
} CALL LikeM2000
</lang>
Maple
<lang Maple> numtheory:-divisors(n); </lang>
Mathematica / Wolfram Language
<lang Mathematica>Factorize[n_Integer] := Divisors[n]</lang>
MATLAB / Octave
<lang Matlab> function fact(n);
f = factor(n); % prime decomposition
K = dec2bin(0:2^length(f)-1)-'0'; % generate all possible permutations
F = ones(1,2^length(f));
for k = 1:size(K)
F(k) = prod(f(~K(k,:))); % and compute products
end;
F = unique(F); % eliminate duplicates
printf('There are %i factors for %i.\n',length(F),n);
disp(F);
end;
</lang>
- Output:
>> fact(12)
There are 6 factors for 12.
1 2 3 4 6 12
>> fact(28)
There are 6 factors for 28.
1 2 4 7 14 28
>> fact(64)
There are 7 factors for 64.
1 2 4 8 16 32 64
>>fact(53)
There are 2 factors for 53.
1 53
Maxima
The builtin divisors function does this.
<lang maxima>(%i96) divisors(100);
(%o96) {1,2,4,5,10,20,25,50,100}</lang>
Such a function could be implemented like so: <lang maxima>divisors2(n) := map( lambda([l], lreduce("*", l)),
apply( cartesian_product,
map( lambda([fac],
setify(makelist(fac[1]^i, i, 0, fac[2]))),
ifactors(n))));</lang>
MAXScript
<lang MAXScript> fn factors n = ( return (for i = 1 to n+1 where mod n i == 0 collect i) ) </lang>
- Output:
<lang MAXScript> factors 3
- (1, 3)
factors 7
- (1, 7)
factors 14
- (1, 2, 7, 14)
factors 60
- (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
factors 54
- (1, 2, 3, 6, 9, 18, 27, 54)
</lang>
Mercury
Mercury is both a logic language and a functional language. As such there are two possible interfaces for calculating the factors of an integer. This code shows both styles of implementation. Note that much of the code here is ceremony put in place to have this be something which can actually compile. The actual factoring is contained in the predicate factor/2 and in the function factor/1. The function form is implemented in terms of the predicate form rather than duplicating all of the predicate code.
The predicates main/2 and factor/2 are shown with the combined type and mode statement (e.g. int::in) as is the usual case for simple predicates with only one mode. This makes the code more immediately understandable. The predicate factor/5, however, has its mode broken out onto a separate line both to show Mercury's mode statement (useful for predicates which can have varying instantiation of parameters) and to stop the code from extending too far to the right. Finally the function factor/1 has its mode statements removed (shown underneath in a comment for illustration purposes) because good coding style (and the default of the compiler!) has all parameters "in"-moded and the return value "out"-moded.
This implementation of factoring works as follows:
- The input number itself and 1 are both considered factors.
- The numbers between 2 and the square root of the input number are checked for even division.
- If the incremental number divides evenly into the input number, both the incremental number and the quotient are added to the list of factors.
This implementation makes use of Mercury's "state variable notation" to keep a pair of variables for accumulation, thus allowing the implementation to be tail recursive. !Accumulator is syntax sugar for a *pair* of variables. One of them is an "in"-moded variable and the other is an "out"-moded variable. !:Accumulator is the "out" portion and !.Accumulator is the "in" portion in the ensuing code.
Using the state variable notation avoids having to keep track of strings of variables unified in the code named things like Acc0, Acc1, Acc2, Acc3, etc.
fac.m
<lang Mercury>:- module fac.
- - interface.
- - import_module io.
- - pred main(io::di, io::uo) is det.
- - implementation.
- - import_module float, int, list, math, string.
main(!IO) :-
io.command_line_arguments(Args, !IO),
list.filter_map(string.to_int, Args, CleanArgs),
list.foldl((pred(Arg::in, !.IO::di, !:IO::uo) is det :-
factor(Arg, X),
io.format("factor(%d, [", [i(Arg)], !IO),
io.write_list(X, ",", io.write_int, !IO),
io.write_string("])\n", !IO)
), CleanArgs, !IO).
- - pred factor(int::in, list(int)::out) is det.
factor(N, Factors) :-
Limit = float.truncate_to_int(math.sqrt(float(N))),
factor(N, 2, Limit, [], Unsorted),
list.sort_and_remove_dups([1, N | Unsorted], Factors).
- - pred factor(int, int, int, list(int), list(int)).
- - mode factor(in, in, in, in, out) is det.
factor(N, X, Limit, !Accumulator) :-
( if X > Limit
then true
else ( if 0 = N mod X
then !:Accumulator = [X, N / X | !.Accumulator]
else true ),
factor(N, X + 1, Limit, !Accumulator) ).
- - func factor(int) = list(int).
%:- mode factor(in) = out is det. factor(N) = Factors :- factor(N, Factors).
- - end_module fac.</lang>
Use and output
Use of the code looks like this:
$ mmc fac.m && ./fac 100 999 12345678 booger factor(100, [1,2,4,5,10,20,25,50,100]) factor(999, [1,3,9,27,37,111,333,999]) factor(12345678, [1,2,3,6,9,18,47,94,141,282,423,846,14593,29186,43779,87558,131337,262674,685871,1371742,2057613,4115226,6172839,12345678])
min
<lang min>(mod 0 ==) :divisor? (() 0 shorten) :new (new (over swons 'pred dip) pick times nip) :iota
(
:n n sqrt int iota ; Only consider numbers up to sqrt(n). (n swap divisor?) filter =f1 f1 (n swap div) map reverse =f2 ; "Mirror" the list of divisors at sqrt(n). (f1 last f2 first ==) (f2 rest #f2) when ; Handle perfect squares. f1 f2 concat
) :factors
24 factors puts! 9 factors puts! 11 factors puts!</lang>
MiniScript
<lang MiniScript>factors = function(n)
result = [1]
for i in range(2, n)
if n % i == 0 then result.push i
end for
return result
end function
while true
n = val(input("Number to factor (0 to quit)? "))
if n <= 0 then break
print factors(n)
end while</lang>
- Output:
Number to factor (0 to quit)? 42 [1, 2, 3, 6, 7, 14, 21, 42] Number to factor (0 to quit)? 101 [1, 101] Number to factor (0 to quit)? 360 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360] Number to factor (0 to quit)? 0
МК-61/52
П9 1 П6 КИП6 ИП9 ИП6 / П8 ^ [x] x#0 21 - x=0 03 ИП6 С/П ИП8 П9 БП 04 1 С/П БП 21
MUMPS
<lang MUMPS>factors(num) New fctr,list,sep,sqrt If num<1 Quit "Too small a number" If num["." Quit "Not an integer" Set sqrt=num**0.5\1 For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1 Set (list,fctr)="",sep="[" For Set fctr=$Order(list(fctr)) Quit:fctr="" Set list=list_sep_fctr,sep="," Quit list_"]"
w $$factors(45) ; [1,3,5,9,15,45] w $$factors(53) ; [1,53] w $$factors(64) ; [1,2,4,8,16,32,64]</lang>
Nanoquery
<lang Nanoquery>n = int(input())
for i in range(1, n / 2) if (n % i = 0) print i + " " end end println n</lang>
NetRexx
<lang NetRexx>/* NetRexx ***********************************************************
- 21.04.2013 Walter Pachl
- 21.04.2013 add method main to accept argument(s)
- /
options replace format comments java crossref symbols nobinary class divl
method main(argwords=String[]) static
arg=Rexx(argwords)
Parse arg a b
Say a b
If a= Then Do
help='java divl low [high] shows'
help=help||' divisors of all numbers between low and high'
Say help
Return
End
If b= Then b=a
loop x=a To b
say x '->' divs(x)
End
method divs(x) public static returns Rexx
if x==1 then return 1 /*handle special case of 1 */
lo=1
hi=x
odd=x//2 /* 1 if x is odd */
loop j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */</lang>
- Output:
java divl 1 10 1 -> 1 2 -> 1 2 3 -> 1 3 4 -> 1 2 4 5 -> 1 5 6 -> 1 2 3 6 7 -> 1 7 8 -> 1 2 4 8 9 -> 1 3 9 10 -> 1 2 5 10
Nim
<lang nim>import intsets, math, algorithm
proc factors(n: int): seq[int] =
var fs: IntSet
for x in 1 .. int(sqrt(float(n))):
if n mod x == 0:
fs.incl(x)
fs.incl(n div x)
for x in fs:
result.add(x)
result.sort()
echo factors(45)</lang>
Niue
<lang Niue>[ 'n ; [ negative-or-zero [ , ] if
[ n not-factor [ , ] when ] else ] n times n ] 'factors ;
[ dup 0 <= ] 'negative-or-zero ; [ swap dup rot swap mod 0 = not ] 'not-factor ;
( tests ) 100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline 53 factors .s .clr ( => 1 53 ) newline 64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline 12 factors .s .clr ( => 1 2 3 4 6 12 ) </lang>
Oberon-2
Oxford Oberon-2 <lang oberon2> MODULE Factors; IMPORT Out,SYSTEM; TYPE LIPool = POINTER TO ARRAY OF LONGINT; LIVector= POINTER TO LIVectorDesc; LIVectorDesc = RECORD cap: INTEGER; len: INTEGER; LIPool: LIPool; END;
PROCEDURE New(cap: INTEGER): LIVector; VAR v: LIVector; BEGIN NEW(v); v.cap := cap; v.len := 0; NEW(v.LIPool,cap); RETURN v END New;
PROCEDURE (v: LIVector) Add(x: LONGINT); VAR newLIPool: LIPool; BEGIN IF v.len = LEN(v.LIPool^) THEN (* run out of space *) v.cap := v.cap + (v.cap DIV 2); NEW(newLIPool,v.cap); SYSTEM.MOVE(SYSTEM.ADR(v.LIPool^),SYSTEM.ADR(newLIPool^),v.cap * SIZE(LONGINT)); v.LIPool := newLIPool END; v.LIPool[v.len] := x; INC(v.len) END Add;
PROCEDURE (v: LIVector) At(idx: INTEGER): LONGINT; BEGIN RETURN v.LIPool[idx]; END At;
PROCEDURE Factors(n:LONGINT): LIVector;
VAR
j: LONGINT;
v: LIVector;
BEGIN
v := New(16);
FOR j := 1 TO n DO
IF (n MOD j) = 0 THEN v.Add(j) END;
END;
RETURN v
END Factors;
VAR v: LIVector; j: INTEGER; BEGIN v := Factors(123); FOR j := 0 TO v.len - 1 DO Out.LongInt(v.At(j),4);Out.Ln END; Out.Int(v.len,6);Out.String(" factors");Out.Ln END Factors. </lang>
- Output:
1
3
41
123
4 factors
Objeck
<lang objeck>use IO; use Structure;
bundle Default {
class Basic {
function : native : GenerateFactors(n : Int) ~ IntVector {
factors := IntVector->New();
factors-> AddBack(1);
factors->AddBack(n);
for(i := 2; i * i <= n; i += 1;) {
if(n % i = 0) {
factors->AddBack(i);
if(i * i <> n) {
factors->AddBack(n / i);
};
};
};
factors->Sort();
return factors;
}
function : Main(args : String[]) ~ Nil {
numbers := [3135, 45, 60, 81];
for(i := 0; i < numbers->Size(); i += 1;) {
factors := GenerateFactors(numbers[i]);
Console->GetInstance()->Print("Factors of ")->Print(numbers[i])->PrintLine(" are:");
each(i : factors) {
Console->GetInstance()->Print(factors->Get(i))->Print(", ");
};
"\n\n"->Print();
};
}
}
}</lang>
OCaml
<lang ocaml>let rec range = function 0 -> [] | n -> range(n-1) @ [n]
let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)</lang>
Oforth
<lang Oforth>Integer method: factors self seq filter(#[ self isMultiple ]) ;
120 factors println</lang>
- Output:
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]
Oz
<lang oz>declare
fun {Factors N}
Sqr = {Float.toInt {Sqrt {Int.toFloat N}}}
Fs = for X in 1..Sqr append:App do
if N mod X == 0 then
CoFactor = N div X
in
if CoFactor == X then %% avoid duplicate factor
{App [X]} %% when N is a square number
else
{App [X CoFactor]}
end
end
end
in
{Sort Fs Value.'<'}
end
in
{Show {Factors 53}}</lang>
Panda
Panda has a factor function already, it's defined as: <lang panda>fun factor(n) type integer->integer
f where n.mod(1..n=>f)==0
45.factor</lang>
PARI/GP
<lang parigp>divisors(n)</lang>
Pascal
<lang pascal>program Factors; var
i, number: integer;
begin
write('Enter a number between 1 and 2147483647: ');
readln(number);
for i := 1 to round(sqrt(number)) - 1 do
if number mod i = 0 then
write (i, ' ', number div i, ' ');
// Check to see if number is a square
i := round(sqrt(number));
if i*i = number then
write(i)
else if number mod i = 0 then
write(i, number/i);
writeln;
end.</lang>
- Output:
Enter a number between 1 and 2147483647: 49 1 49 7 Enter a number between 1 and 2147483647: 353435 1 25755 3 8585 5 5151 15 1717 17 1515 51 505 85 303 101 255
using Prime decomposition
like [C Prime_factoring].
Insertion sort was much faster, because mostly not so many factors need to be sorted.
"runtime overhead" +25% instead +100% for quicksort against no sort.
Especially fast for consecutive integers.
<lang pascal>program FacOfInt;
// gets factors of consecutive integers fast
// limited to 1.2e11
{$IFDEF FPC}
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils
{$IFDEF WINDOWS},Windows{$ENDIF}
;
//###################################################################### //prime decomposition const //HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1
HCN_DivCnt = 4096;
type
tItem = Uint64; tDivisors = array [0..HCN_DivCnt] of tItem; tpDivisor = pUint64;
const
//used odd size for test only SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache
type
tdigits = array [0..31] of Uint32;
//the first number with 11 different prime factors =
//2*3*5*7*11*13*17*19*23*29*31 = 2E11
//56 byte
tprimeFac = packed record
pfSumOfDivs,
pfRemain : Uint64;
pfDivCnt : Uint32;
pfMaxIdx : Uint32;
pfpotPrimIdx : array[0..9] of word;
pfpotMax : array[0..11] of byte;
end;
tpPrimeFac = ^tprimeFac;
tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac; tPrimes = array[0..65535] of Uint32;
var
{$ALIGN 8}
SmallPrimes: tPrimes;
{$ALIGN 32}
PrimeDecompField :tPrimeDecompField;
pdfIDX,pdfOfs: NativeInt;
procedure InitSmallPrimes; //get primes. #0..65535.Sieving only odd numbers const
MAXLIMIT = (821641-1) shr 1;
var
pr : array[0..MAXLIMIT] of byte; p,j,d,flipflop :NativeUInt;
Begin
SmallPrimes[0] := 2;
fillchar(pr[0],SizeOf(pr),#0);
p := 0;
repeat
repeat
p +=1
until pr[p]= 0;
j := (p+1)*p*2;
if j>MAXLIMIT then
BREAK;
d := 2*p+1;
repeat
pr[j] := 1;
j += d;
until j>MAXLIMIT;
until false;
SmallPrimes[1] := 3;
SmallPrimes[2] := 5;
j := 3;
d := 7;
flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
p := 3;
repeat
if pr[p] = 0 then
begin
SmallPrimes[j] := d;
inc(j);
end;
d += 2*flipflop;
p+=flipflop;
flipflop := 3-flipflop;
until (p > MAXLIMIT) OR (j>High(SmallPrimes));
end;
function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring; var
s: String[31]; chk,p,i: NativeInt;
Begin
str(n,s);
result := s+' :';
with pd^ do
begin
str(pfDivCnt:3,s);
result += s+' : ';
chk := 1;
For n := 0 to pfMaxIdx-1 do
Begin
if n>0 then
result += '*';
p := SmallPrimes[pfpotPrimIdx[n]];
chk *= p;
str(p,s);
result += s;
i := pfpotMax[n];
if i >1 then
Begin
str(pfpotMax[n],s);
result += '^'+s;
repeat
chk *= p;
dec(i);
until i <= 1;
end;
end;
p := pfRemain;
If p >1 then
Begin
str(p,s);
chk *= p;
result += '*'+s;
end;
str(chk,s);
result += '_chk_'+s+'<';
str(pfSumOfDivs,s);
result += '_SoD_'+s+'<';
end;
end;
function smplPrimeDecomp(n:Uint64):tprimeFac; var
pr,i,pot,fac,q :NativeUInt;
Begin
with result do Begin pfDivCnt := 1; pfSumOfDivs := 1; pfRemain := n; pfMaxIdx := 0; pfpotPrimIdx[0] := 1; pfpotMax[0] := 0;
i := 0;
while i < High(SmallPrimes) do
begin
pr := SmallPrimes[i];
q := n DIV pr;
//if n < pr*pr
if pr > q then
BREAK;
if n = pr*q then
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pot := 0;
fac := pr;
repeat
n := q;
q := n div pr;
pot+=1;
fac *= pr;
until n <> pr*q;
pfpotMax[pfMaxIdx] := pot;
pfDivCnt *= pot+1;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
end;
inc(i);
end;
pfRemain := n;
if n > 1 then
Begin
pfDivCnt *= 2;
pfSumOfDivs *= n+1
end;
end;
end;
function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt; //n must be multiple of base aka n mod base must be 0 var
q,r: Uint64; i : NativeInt;
Begin
fillchar(dgt,SizeOf(dgt),#0); i := 0; n := n div base; result := 0; repeat r := n; q := n div base; r -= q*base; n := q; dgt[i] := r; inc(i); until (q = 0); //searching lowest pot in base result := 0; while (result<i) AND (dgt[result] = 0) do inc(result); inc(result);
end;
function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt; var
q :NativeInt;
Begin
result := 0;
q := dgt[result]+1;
if q = base then
repeat
dgt[result] := 0;
inc(result);
q := dgt[result]+1;
until q <> base;
dgt[result] := q;
result +=1;
end;
function SieveOneSieve(var pdf:tPrimeDecompField):boolean; var
dgt:tDigits; i,j,k,pr,fac,n,MaxP : Uint64;
begin
n := pdfOfs;
if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then
EXIT(FALSE);
//init
for i := 0 to SizePrDeFe-1 do
begin
with pdf[i] do
Begin
pfDivCnt := 1;
pfSumOfDivs := 1;
pfRemain := n+i;
pfMaxIdx := 0;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := 0;
end;
end;
//first factor 2. Make n+i even
i := (pdfIdx+n) AND 1;
IF (n = 0) AND (pdfIdx<2) then
i := 2;
repeat
with pdf[i] do
begin
j := BsfQWord(n+i);
pfMaxIdx := 1;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := j;
pfRemain := (n+i) shr j;
pfSumOfDivs := (Uint64(1) shl (j+1))-1;
pfDivCnt := j+1;
end;
i += 2;
until i >=SizePrDeFe;
//i now index in SmallPrimes
i := 0;
maxP := trunc(sqrt(n+SizePrDeFe))+1;
repeat
//search next prime that is in bounds of sieve
if n = 0 then
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if k < SizePrDeFe then
break;
until pr > MaxP;
end
else
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if (k = pr) AND (n>0) then
k:= 0;
if k < SizePrDeFe then
break;
until pr > MaxP;
end;
//no need to use higher primes
if pr*pr > n+SizePrDeFe then
BREAK;
//j is power of prime
j := CnvtoBASE(dgt,n+k,pr);
repeat
with pdf[k] do
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pfpotMax[pfMaxIdx] := j;
pfDivCnt *= j+1;
fac := pr;
repeat
pfRemain := pfRemain DIV pr;
dec(j);
fac *= pr;
until j<= 0;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
k += pr;
j := IncByBaseInBase(dgt,pr);
end;
until k >= SizePrDeFe;
until false;
//correct sum of & count of divisors
for i := 0 to High(pdf) do
Begin
with pdf[i] do
begin
j := pfRemain;
if j <> 1 then
begin
pfSumOFDivs *= (j+1);
pfDivCnt *=2;
end;
end;
end;
result := true;
end;
function NextSieve:boolean; begin
dec(pdfIDX,SizePrDeFe); inc(pdfOfs,SizePrDeFe); result := SieveOneSieve(PrimeDecompField);
end;
function GetNextPrimeDecomp:tpPrimeFac; begin
if pdfIDX >= SizePrDeFe then
if Not(NextSieve) then
EXIT(NIL);
result := @PrimeDecompField[pdfIDX];
inc(pdfIDX);
end;
function Init_Sieve(n:NativeUint):boolean; //Init Sieve pdfIdx,pdfOfs are Global begin
pdfIdx := n MOD SizePrDeFe; pdfOfs := n-pdfIdx; result := SieveOneSieve(PrimeDecompField);
end;
procedure InsertSort(pDiv:tpDivisor; Left, Right : NativeInt ); var
I, J: NativeInt; Pivot : tItem;
begin
for i:= 1 + Left to Right do
begin
Pivot:= pDiv[i];
j:= i - 1;
while (j >= Left) and (pDiv[j] > Pivot) do
begin
pDiv[j+1]:=pDiv[j];
Dec(j);
end;
pDiv[j+1]:= pivot;
end;
end;
procedure GetDivisors(pD:tpPrimeFac;var Divs:tDivisors); var
pDivs : tpDivisor; pPot : UInt64; i,len,j,l,p,k: Int32;
Begin
pDivs := @Divs[0];
pDivs[0] := 1;
len := 1;
l := 1;
with pD^ do
Begin
For i := 0 to pfMaxIdx-1 do
begin
//Multiply every divisor before with the new primefactors
//and append them to the list
k := pfpotMax[i];
p := SmallPrimes[pfpotPrimIdx[i]];
pPot :=1;
repeat
pPot *= p;
For j := 0 to len-1 do
Begin
pDivs[l]:= pPot*pDivs[j];
inc(l);
end;
dec(k);
until k<=0;
len := l;
end;
p := pfRemain;
If p >1 then
begin
For j := 0 to len-1 do
Begin
pDivs[l]:= p*pDivs[j];
inc(l);
end;
len := l;
end;
end;
//Sort. Insertsort much faster than QuickSort in this special case
InsertSort(pDivs,0,len-1);
//end marker
pDivs[len] :=0;
end;
procedure AllFacsOut(var Divs:tdivisors;proper:boolean=true); var
k,j: Int32;
Begin
k := 0;
j := 1;
if Proper then
j:= 2;
repeat
IF Divs[j] = 0 then
BREAK;
write(Divs[k],',');
inc(j);
inc(k);
until false;
writeln(Divs[k]);
end;
var
pPrimeDecomp :tpPrimeFac; Mypd : tPrimeFac; Divs:tDivisors; T0:Int64; n : NativeUInt;
Begin
InitSmallPrimes;
T0 := GetTickCount64;
n := 0;
Init_Sieve(0);
repeat
pPrimeDecomp:= GetNextPrimeDecomp;
GetDivisors(pPrimeDecomp,Divs);
inc(n);
until n > 10*1000*1000+1;
T0 := GetTickCount64-T0;
writeln('runtime ',T0/1000:0:3,' s');
GetDivisors(pPrimeDecomp,Divs);
AllFacsOut(Divs,true);
AllFacsOut(Divs,false);
writeln('simple version');
T0 := GetTickCount64;
n := 0;
repeat
Mypd:= smplPrimeDecomp(n);
GetDivisors(@Mypd,Divs);
inc(n);
until n > 10*1000*1000+1;
T0 := GetTickCount64-T0;
writeln('runtime ',T0/1000:0:3,' s');
GetDivisors(@Mypd,Divs);
AllFacsOut(Divs,true);
AllFacsOut(Divs,false);
end.</lang>
- Output:
TIO.RUN //out-commented GetDivisors, but still calculates sum of divisors and count of divisors runtime 0.555 s 1,11,909091 1,11,909091,10000001 simple version runtime 8.167 s 1,11,909091 1,11,909091,10000001 Real time: 8.868 s CPU share: 99.57 % //with GetDivisors runtime 1.815 s 1,11,909091 1,11,909091,10000001 simple version runtime 11.057 s 1,11,909091 1,11,909091,10000001 Real time: 13.082 s CPU share: 99.16 %
Perl
<lang perl>sub factors {
my($n) = @_;
return grep { $n % $_ == 0 }(1 .. $n);
} print join ' ',factors(64), "\n";</lang>
Or more intelligently:
<lang perl>sub factors {
my $n = shift;
$n = -$n if $n < 0;
my @divisors;
for (1 .. int(sqrt($n))) { # faster and less memory than map/grep
push @divisors, $_ unless $n % $_;
}
# Return divisors including top half, without duplicating a square
@divisors, map { $_*$_ == $n ? () : int($n/$_) } reverse @divisors;
} print join " ", factors(64), "\n";</lang>
One could also use a module, e.g.:
<lang perl>use ntheory qw/divisors/; print join " ", divisors(12345678), "\n";
- Alternately something like: fordivisors { say } 12345678; </lang>
Phix
There is a builtin factors(n), which takes an optional second parameter to include 1 and n:
?factors(12345,1)
- Output:
{1,3,5,15,823,2469,4115,12345}
You can find the implementation of factors() and prime_factors() in builtins\pfactors.e
PHP
<lang PHP>function GetFactors($n){
$factors = array(1, $n);
for($i = 2; $i * $i <= $n; $i++){
if($n % $i == 0){
$factors[] = $i;
if($i * $i != $n)
$factors[] = $n/$i;
}
}
sort($factors);
return $factors;
}</lang>
PicoLisp
<lang PicoLisp>(de factors (N)
(filter
'((D) (=0 (% N D)))
(range 1 N) ) )</lang>
PILOT
<lang pilot>T :Enter a number. A :#n C :factor = 1 T :The factors of #n are:
- Loop
C :remainder = n % factor T ( remainder = 0 ) :#factor J ( factor = n ) :*Finished C :factor = factor + 1 J :*Loop
- Finished
END:</lang>
PL/I
<lang pli>factors: procedure options(main);
declare i binary( 15 )fixed;
declare n binary( 15 )fixed;
do n = 90 to 100;
put skip list( 'factors of: ', n, ': ' );
do i = 1 to n;
if mod(n, i) = 0 then put edit( i )(f(4));
end;
end;
end factors; </lang>
- Output:
factors of: 90 : 1 2 3 5 6 9 10 15 18 30 45 90 factors of: 91 : 1 7 13 91 factors of: 92 : 1 2 4 23 46 92 factors of: 93 : 1 3 31 93 factors of: 94 : 1 2 47 94 factors of: 95 : 1 5 19 95 factors of: 96 : 1 2 3 4 6 8 12 16 24 32 48 96 factors of: 97 : 1 97 factors of: 98 : 1 2 7 14 49 98 factors of: 99 : 1 3 9 11 33 99 factors of: 100 : 1 2 4 5 10 20 25 50 100
See also #Polyglot:PL/I and PL/M
PL/M
Plain English
<lang plainenglish>To run: Start up. Show the factors of 11. Show the factors of 21. Show the factors of 519. Wait for the escape key. Shut down.
To show the factors of a number: Write "The factors of " then the number then ":" on the console. Find a square root of the number. Loop. If a counter is past the square root, write "" on the console; exit. Divide the number by the counter giving a quotient and a remainder. If the remainder is 0, show the counter and the quotient. Repeat.
A factor is a number.
To show a factor and another factor: If the factor is not the other factor, write "" then the factor then " " then the other factor then " " on the console without advancing; exit. Write "" then the factor on the console without advancing.</lang>
- Output:
The factors of 11: 1 11 The factors of 21: 1 21 3 7 The factors of 519: 1 519 3 173
Polyglot:PL/I and PL/M
... under CP/M (or an emulator)
Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page.
Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.
<lang pli>factors_100H: procedure options (main);
/* PL/I DEFINITIONS */ %include 'pg.inc'; /* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /*
DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
DECLARE SADDR LITERALLY '.', BIT LITERALLY 'BYTE';
DECLARE FIXED LITERALLY ' ';
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRCHAR: PROCEDURE( C ); DECLARE C CHARACTER; CALL BDOS( 2, C ); END;
PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
PRNUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
N$STR( W := LAST( N$STR ) ) = '$';
N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL BDOS( 9, .N$STR( W ) );
END PRNUMBER;
MODF: PROCEDURE( A, B )ADDRESS;
DECLARE ( A, B )ADDRESS;
RETURN( A MOD B );
END MODF;
/* END LANGUAGE DEFINITIONS */
/* TASK */
DECLARE ( I, N ) FIXED BINARY;
DO N = 90 TO 100;
CALL PRSTRING( SADDR( 'FACTORS OF: $' ) );
CALL PRNUMBER( N );
CALL PRCHAR( ':' );
DO I = 1 TO N;
IF MODF( N, I ) = 0 THEN DO;
CALL PRCHAR( ' ' );
CALL PRNUMBER( I );
END;
END;
CALL PRNL;
END;
EOF: end factors_100H;</lang>
- Output:
FACTORS OF: 90: 1 2 3 5 6 9 10 15 18 30 45 90 FACTORS OF: 91: 1 7 13 91 FACTORS OF: 92: 1 2 4 23 46 92 FACTORS OF: 93: 1 3 31 93 FACTORS OF: 94: 1 2 47 94 FACTORS OF: 95: 1 5 19 95 FACTORS OF: 96: 1 2 3 4 6 8 12 16 24 32 48 96 FACTORS OF: 97: 1 97 FACTORS OF: 98: 1 2 7 14 49 98 FACTORS OF: 99: 1 3 9 11 33 99 FACTORS OF: 100: 1 2 4 5 10 20 25 50 100
PowerShell
Straightforward but slow
<lang powershell>function Get-Factor ($a) {
1..$a | Where-Object { $a % $_ -eq 0 }
}</lang>
This one uses a range of integers up to the target number and just filters it using the Where-Object cmdlet. It's very slow though, so it is not very usable for larger numbers.
A little more clever
<lang powershell>function Get-Factor ($a) {
1..[Math]::Sqrt($a) `
| Where-Object { $a % $_ -eq 0 } `
| ForEach-Object { $_; $a / $_ } `
| Sort-Object -Unique
}</lang> Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier.
ProDOS
Uses the math module: <lang ProDOS>editvar /newvar /value=a /userinput=1 /title=Enter an integer: do /delimspaces %% -a- >b printline Factors of -a-: -b- </lang>
Prolog
Simple Brute Force Implementation <lang Prolog> brute_force_factors( N , Fs ) :-
integer(N) , N > 0 , setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs ) .
</lang>
A Slightly Smarter Implementation <lang Prolog> smart_factors(N,Fs) :-
integer(N) , N > 0 , setof( F , factor(N,F) , Fs ) .
factor(N,F) :-
L is floor(sqrt(N)) , between(1,L,X) , 0 =:= N mod X , ( F = X ; F is N // X ) .
</lang>
Not every Prolog has between/3: you might need this:
<lang Prolog>
between(X,Y,Z) :-
integer(X) , integer(Y) , X =< Z , between1(X,Y,Z) .
between1(X,Y,X) :-
X =< Y .
between1(X,Y,Z) :-
X < Y , X1 is X+1 , between1(X1,Y,Z) .
</lang>
- Output:
?- N=36 ,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] ; N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] . ?- N=53,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 53, Factors = [1, 53] ; N = 53, Factors = [1, 53] . ?- N=100,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] ; N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] . ?- N=144,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] ; N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] . ?- N=32765,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32765, Factors = [1, 5, 6553, 32765] ; N = 32765, Factors = [1, 5, 6553, 32765] . ?- N=32766,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] ; N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] . 38 ?- N=32767,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] ; N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] .
PureBasic
<lang PureBasic>Procedure PrintFactors(n)
Protected i, lim=Round(sqr(n),#PB_Round_Up)
NewList F.i()
For i=1 To lim
If n%i=0
AddElement(F()): F()=i
AddElement(F()): F()=n/i
EndIf
Next
;- Present the result
SortList(F(),#PB_Sort_Ascending)
ForEach F()
Print(str(F())+" ")
Next
EndProcedure
If OpenConsole()
Print("Enter integer to factorize: ")
PrintFactors(Val(Input()))
Print(#CRLF$+#CRLF$+"Press ENTER to quit."): Input()
EndIf</lang>
- Output:
Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96
Python
Naive and slow but simplest (check all numbers from 1 to n): <lang python>>>> def factors(n):
return [i for i in range(1, n + 1) if not n%i]</lang>
Slightly better (realize that there are no factors between n/2 and n): <lang python>>>> def factors(n):
return [i for i in range(1, n//2 + 1) if not n%i] + [n]
>>> factors(45) [1, 3, 5, 9, 15, 45]</lang>
Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)): <lang python>>>> from math import sqrt >>> def factor(n):
factors = set()
for x in range(1, int(sqrt(n)) + 1):
if n % x == 0:
factors.add(x)
factors.add(n//x)
return sorted(factors)
>>> for i in (45, 53, 64): print( "%i: factors: %s" % (i, factor(i)) )
45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]</lang>
More efficient when factoring many numbers: <lang python>from itertools import chain, cycle, accumulate # last of which is Python 3 only
def factors(n):
def prime_powers(n):
# c goes through 2, 3, 5, then the infinite (6n+1, 6n+5) series
for c in accumulate(chain([2, 1, 2], cycle([2,4]))):
if c*c > n: break
if n%c: continue
d,p = (), c
while not n%c:
n,p,d = n//c, p*c, d + (p,)
yield(d)
if n > 1: yield((n,))
r = [1]
for e in prime_powers(n):
r += [a*b for a in r for b in e]
return r</lang>
Quackery
isqrt returns the integer square root and remainder (i.e. the square root of 11 is 3 remainder 2, because three squared plus two equals eleven.) If the number is a perfect square the remainder is zero. This is used to remove a duplicate factor from the list of factors which is generated when finding the factors of a perfect square.
The nest editing at the end of the definition (i.e. the code after the drop on a line by itself) removes a duplicate factor if there is one, and arranges the factors in ascending numerical order at the same time.
<lang> [ 1
[ 2dup < not while
2 << again ]
0
[ over 1 > while
dip [ 2 >> 2dup - ]
dup 1 >> unrot -
dup 0 < iff drop
else
[ 2swap nip
rot over + ]
again ] nip swap ] is isqrt ( n --> n n )
[ [] swap
dup isqrt 0 = dip
[ times
[ dup i^ 1+ /mod iff
drop done
rot join
i^ 1+ join swap ]
drop
dup size 2 / split ]
if [ -1 split drop ]
swap join ] is factors ( n --> [ )
20 times
[ i^ 1+ dup
dup 10 < if sp
echo
say ": "
factors witheach
[ echo i if say ", " ]
cr ]</lang>
- Output:
1: 1 2: 1, 2 3: 1, 3 4: 1, 2, 4 5: 1, 5 6: 1, 2, 3, 6 7: 1, 7 8: 1, 2, 4, 8 9: 1, 3, 9 10: 1, 2, 5, 10 11: 1, 11 12: 1, 2, 3, 4, 6, 12 13: 1, 13 14: 1, 2, 7, 14 15: 1, 3, 5, 15 16: 1, 2, 4, 8, 16 17: 1, 17 18: 1, 2, 3, 6, 9, 18 19: 1, 19 20: 1, 2, 4, 5, 10, 20
R
Array solution
<lang rsplus>factors <- function(n) {
if(length(n) > 1)
{
lapply(as.list(n), factors)
} else
{
one.to.n <- seq_len(n)
one.to.n[(n %% one.to.n) == 0]
}
}</lang>
- Output:
>factors(60) [1] 1 2 3 4 5 6 10 12 15 20 30 60 >factors(c(45, 53, 64)) [[1]] [1] 1 3 5 9 15 45 [[2]] [1] 1 53 [[3]] [1] 1 2 4 8 16 32 64
Filter solution
With identical output, a more idiomatic way is to use R's Filter. <lang rsplus>factors <- function(n) c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n)
- Vectorize is an interesting alternative to the previous solution's lapply.
manyFactors <- function(vec) Vectorize(factors)(vec)</lang>
Racket
<lang Racket>
- lang racket
- a naive version
(define (naive-factors n)
(for/list ([i (in-range 1 (add1 n))] #:when (zero? (modulo n i))) i))
(naive-factors 120) ; -> '(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)
- much better
- use `factorize' to get prime factors and construct the
- list of results from that
(require math) (define (factors n)
(sort (for/fold ([l '(1)]) ([p (factorize n)])
(append (for*/list ([e (in-range 1 (add1 (cadr p)))] [x l])
(* x (expt (car p) e)))
l))
<))
(naive-factors 120) ; -> same
- to see how fast it is
(define huge 1200034005600070000008900000000000000000) (time (length (factors huge)))
- I get 42ms for getting a list of 7776 numbers
- but actually the math library comes with a `divisors' function that
- does the same, except even faster
(divisors 120) ; -> same
(time (length (divisors huge)))
- And this one clocks at 17ms
</lang>
Raku
(formerly Perl 6)
<lang perl6>sub factors (Int $n) { (1..$n).grep($n %% *) }</lang>
REALbasic
<lang vb>Function factors(num As UInt64) As UInt64()
'This function accepts an unsigned 64 bit integer as input and returns an array of unsigned 64 bit integers
Dim result() As UInt64
Dim iFactor As UInt64 = 1
While iFactor <= num/2 'Since a factor will never be larger than half of the number
If num Mod iFactor = 0 Then
result.Append(iFactor)
End If
iFactor = iFactor + 1
Wend
result.Append(num) 'Since a given number is always a factor of itself
Return result
End Function</lang>
Red
<lang Red>Red []
factors: function [n [integer!]] [
n: absolute n
collect [
repeat i (sq: sqrt n) - 1 [
if n % i = 0 [
keep i
keep n / i
]
]
if sq = sq: to-integer sq [keep sq]
]
]
foreach num [
24 -64 ; negative 64 ; square 101 ; prime 123456789 ; large
][
print mold/flat sort factors num
]</lang>
Relation
<lang Relation> program factors(num) relation fact insert 1 set i = 2 while i < num / 2 if num / i = floor(num/i) insert i end if set i = i + 1 end while insert num print end program </lang>
REXX
optimized version
This REXX version has no effective limits on the number of decimal digits in the number to be factored [by adjusting the number of digits (precision)].
This REXX version also supports negative integers and zero.
It also indicates primes in the output listing as well as the number of divisors.
It also displays a final count of the number of primes found.
This REXX version is about 22% faster than the alternate REXX version (2nd version). <lang rexx>/*REXX program displays divisors of any [negative/zero/positive] integer or a range.*/ parse arg LO HI inc . /*obtain the optional args*/ HI= word(HI LO 20, 1); LO= word(LO 1,1); inc= word(inc 1,1) /*define the range options*/ w= length(HI) + 2; numeric digits max(9, w-2); != '∞' /*decimal digits for // */ @.=left(,7); @.1= "{unity}"; @.2= '[prime]'; @.!= " {∞} " /*define some literals. */ say center('n', w) "#divisors" center('divisors', 60) /*display the header. */ say copies('═', w) "═════════" copies('═' , 60) /* " " separator. */ pn= 0 /*count of prime numbers. */
do k=2 until sq.k>=HI; sq.k= k*k /*memoization for squares.*/
end /*k*/
do n=LO to HI by inc; $= divs(n); #= words($) /*get list of divs; # divs*/
if $==! then do; #= !; $= ' (infinite)'; end /*handle case for infinity*/
p= @.#; if n<0 then if n\==-1 then p= @.. /* " " " negative*/
if p==@.2 then pn= pn + 1 /*Prime? Then bump counter*/
say center(n, w) center('['#"]", 9) "──► " p ' ' $
end /*n*/ /* [↑] process a range of integers. */
say say right(pn, 20) ' primes were found.' /*display the number of primes found. */ exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ divs: procedure expose sq.; parse arg x 1 b; a=1 /*set X and B to the 1st argument. */
if x<2 then do; x= abs(x); if x==1 then return 1; if x==0 then return '∞'; b=x
end
odd= x // 2 /* [↓] process EVEN or ODD ints. ___*/
do j=2+odd by 1+odd while sq.j<x /*divide by all the integers up to √ x */
if x//j==0 then do; a=a j; b=x%j b; end /*÷? Add divisors to α and ß lists*/
end /*j*/ /* [↑] % ≡ integer division. ___*/
if sq.j==x then return a j b /*Was X a square? Then insert √ x */
return a b /*return the divisors of both lists. */</lang>
- output when using the input of: -6 200
(Shown at 3/4 size.)
n #divisors divisors
══════ ═════════ ════════════════════════════════════════════════════════════
-6 [4] ──► 1 2 3 6
-5 [2] ──► 1 5
-4 [3] ──► 1 2 4
-3 [2] ──► 1 3
-2 [2] ──► 1 2
-1 [1] ──► {unity} 1
0 [∞] ──► {∞} (infinite)
1 [1] ──► {unity} 1
2 [2] ──► [prime] 1 2
3 [2] ──► [prime] 1 3
4 [3] ──► 1 2 4
5 [2] ──► [prime] 1 5
6 [4] ──► 1 2 3 6
7 [2] ──► [prime] 1 7
8 [4] ──► 1 2 4 8
9 [3] ──► 1 3 9
10 [4] ──► 1 2 5 10
11 [2] ──► [prime] 1 11
12 [6] ──► 1 2 3 4 6 12
13 [2] ──► [prime] 1 13
14 [4] ──► 1 2 7 14
15 [4] ──► 1 3 5 15
16 [5] ──► 1 2 4 8 16
17 [2] ──► [prime] 1 17
18 [6] ──► 1 2 3 6 9 18
19 [2] ──► [prime] 1 19
20 [6] ──► 1 2 4 5 10 20
21 [4] ──► 1 3 7 21
22 [4] ──► 1 2 11 22
23 [2] ──► [prime] 1 23
24 [8] ──► 1 2 3 4 6 8 12 24
25 [3] ──► 1 5 25
26 [4] ──► 1 2 13 26
27 [4] ──► 1 3 9 27
28 [6] ──► 1 2 4 7 14 28
29 [2] ──► [prime] 1 29
30 [8] ──► 1 2 3 5 6 10 15 30
31 [2] ──► [prime] 1 31
32 [6] ──► 1 2 4 8 16 32
33 [4] ──► 1 3 11 33
34 [4] ──► 1 2 17 34
35 [4] ──► 1 5 7 35
36 [9] ──► 1 2 3 4 6 9 12 18 36
37 [2] ──► [prime] 1 37
38 [4] ──► 1 2 19 38
39 [4] ──► 1 3 13 39
40 [8] ──► 1 2 4 5 8 10 20 40
41 [2] ──► [prime] 1 41
42 [8] ──► 1 2 3 6 7 14 21 42
43 [2] ──► [prime] 1 43
44 [6] ──► 1 2 4 11 22 44
45 [6] ──► 1 3 5 9 15 45
46 [4] ──► 1 2 23 46
47 [2] ──► [prime] 1 47
48 [10] ──► 1 2 3 4 6 8 12 16 24 48
49 [3] ──► 1 7 49
50 [6] ──► 1 2 5 10 25 50
51 [4] ──► 1 3 17 51
52 [6] ──► 1 2 4 13 26 52
53 [2] ──► [prime] 1 53
54 [8] ──► 1 2 3 6 9 18 27 54
55 [4] ──► 1 5 11 55
56 [8] ──► 1 2 4 7 8 14 28 56
57 [4] ──► 1 3 19 57
58 [4] ──► 1 2 29 58
59 [2] ──► [prime] 1 59
60 [12] ──► 1 2 3 4 5 6 10 12 15 20 30 60
61 [2] ──► [prime] 1 61
62 [4] ──► 1 2 31 62
63 [6] ──► 1 3 7 9 21 63
64 [7] ──► 1 2 4 8 16 32 64
65 [4] ──► 1 5 13 65
66 [8] ──► 1 2 3 6 11 22 33 66
67 [2] ──► [prime] 1 67
68 [6] ──► 1 2 4 17 34 68
69 [4] ──► 1 3 23 69
70 [8] ──► 1 2 5 7 10 14 35 70
71 [2] ──► [prime] 1 71
72 [12] ──► 1 2 3 4 6 8 9 12 18 24 36 72
73 [2] ──► [prime] 1 73
74 [4] ──► 1 2 37 74
75 [6] ──► 1 3 5 15 25 75
76 [6] ──► 1 2 4 19 38 76
77 [4] ──► 1 7 11 77
78 [8] ──► 1 2 3 6 13 26 39 78
79 [2] ──► [prime] 1 79
80 [10] ──► 1 2 4 5 8 10 16 20 40 80
81 [5] ──► 1 3 9 27 81
82 [4] ──► 1 2 41 82
83 [2] ──► [prime] 1 83
84 [12] ──► 1 2 3 4 6 7 12 14 21 28 42 84
85 [4] ──► 1 5 17 85
86 [4] ──► 1 2 43 86
87 [4] ──► 1 3 29 87
88 [8] ──► 1 2 4 8 11 22 44 88
89 [2] ──► [prime] 1 89
90 [12] ──► 1 2 3 5 6 9 10 15 18 30 45 90
91 [4] ──► 1 7 13 91
92 [6] ──► 1 2 4 23 46 92
93 [4] ──► 1 3 31 93
94 [4] ──► 1 2 47 94
95 [4] ──► 1 5 19 95
96 [12] ──► 1 2 3 4 6 8 12 16 24 32 48 96
97 [2] ──► [prime] 1 97
98 [6] ──► 1 2 7 14 49 98
99 [6] ──► 1 3 9 11 33 99
100 [9] ──► 1 2 4 5 10 20 25 50 100
101 [2] ──► [prime] 1 101
102 [8] ──► 1 2 3 6 17 34 51 102
103 [2] ──► [prime] 1 103
104 [8] ──► 1 2 4 8 13 26 52 104
105 [8] ──► 1 3 5 7 15 21 35 105
106 [4] ──► 1 2 53 106
107 [2] ──► [prime] 1 107
108 [12] ──► 1 2 3 4 6 9 12 18 27 36 54 108
109 [2] ──► [prime] 1 109
110 [8] ──► 1 2 5 10 11 22 55 110
111 [4] ──► 1 3 37 111
112 [10] ──► 1 2 4 7 8 14 16 28 56 112
113 [2] ──► [prime] 1 113
114 [8] ──► 1 2 3 6 19 38 57 114
115 [4] ──► 1 5 23 115
116 [6] ──► 1 2 4 29 58 116
117 [6] ──► 1 3 9 13 39 117
118 [4] ──► 1 2 59 118
119 [4] ──► 1 7 17 119
120 [16] ──► 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
121 [3] ──► 1 11 121
122 [4] ──► 1 2 61 122
123 [4] ──► 1 3 41 123
124 [6] ──► 1 2 4 31 62 124
125 [4] ──► 1 5 25 125
126 [12] ──► 1 2 3 6 7 9 14 18 21 42 63 126
127 [2] ──► [prime] 1 127
128 [8] ──► 1 2 4 8 16 32 64 128
129 [4] ──► 1 3 43 129
130 [8] ──► 1 2 5 10 13 26 65 130
131 [2] ──► [prime] 1 131
132 [12] ──► 1 2 3 4 6 11 12 22 33 44 66 132
133 [4] ──► 1 7 19 133
134 [4] ──► 1 2 67 134
135 [8] ──► 1 3 5 9 15 27 45 135
136 [8] ──► 1 2 4 8 17 34 68 136
137 [2] ──► [prime] 1 137
138 [8] ──► 1 2 3 6 23 46 69 138
139 [2] ──► [prime] 1 139
140 [12] ──► 1 2 4 5 7 10 14 20 28 35 70 140
141 [4] ──► 1 3 47 141
142 [4] ──► 1 2 71 142
143 [4] ──► 1 11 13 143
144 [15] ──► 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144
145 [4] ──► 1 5 29 145
146 [4] ──► 1 2 73 146
147 [6] ──► 1 3 7 21 49 147
148 [6] ──► 1 2 4 37 74 148
149 [2] ──► [prime] 1 149
150 [12] ──► 1 2 3 5 6 10 15 25 30 50 75 150
151 [2] ──► [prime] 1 151
152 [8] ──► 1 2 4 8 19 38 76 152
153 [6] ──► 1 3 9 17 51 153
154 [8] ──► 1 2 7 11 14 22 77 154
155 [4] ──► 1 5 31 155
156 [12] ──► 1 2 3 4 6 12 13 26 39 52 78 156
157 [2] ──► [prime] 1 157
158 [4] ──► 1 2 79 158
159 [4] ──► 1 3 53 159
160 [12] ──► 1 2 4 5 8 10 16 20 32 40 80 160
161 [4] ──► 1 7 23 161
162 [10] ──► 1 2 3 6 9 18 27 54 81 162
163 [2] ──► [prime] 1 163
164 [6] ──► 1 2 4 41 82 164
165 [8] ──► 1 3 5 11 15 33 55 165
166 [4] ──► 1 2 83 166
167 [2] ──► [prime] 1 167
168 [16] ──► 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168
169 [3] ──► 1 13 169
170 [8] ──► 1 2 5 10 17 34 85 170
171 [6] ──► 1 3 9 19 57 171
172 [6] ──► 1 2 4 43 86 172
173 [2] ──► [prime] 1 173
174 [8] ──► 1 2 3 6 29 58 87 174
175 [6] ──► 1 5 7 25 35 175
176 [10] ──► 1 2 4 8 11 16 22 44 88 176
177 [4] ──► 1 3 59 177
178 [4] ──► 1 2 89 178
179 [2] ──► [prime] 1 179
180 [18] ──► 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180
181 [2] ──► [prime] 1 181
182 [8] ──► 1 2 7 13 14 26 91 182
183 [4] ──► 1 3 61 183
184 [8] ──► 1 2 4 8 23 46 92 184
185 [4] ──► 1 5 37 185
186 [8] ──► 1 2 3 6 31 62 93 186
187 [4] ──► 1 11 17 187
188 [6] ──► 1 2 4 47 94 188
189 [8] ──► 1 3 7 9 21 27 63 189
190 [8] ──► 1 2 5 10 19 38 95 190
191 [2] ──► [prime] 1 191
192 [14] ──► 1 2 3 4 6 8 12 16 24 32 48 64 96 192
193 [2] ──► [prime] 1 193
194 [4] ──► 1 2 97 194
195 [8] ──► 1 3 5 13 15 39 65 195
196 [9] ──► 1 2 4 7 14 28 49 98 196
197 [2] ──► [prime] 1 197
198 [12] ──► 1 2 3 6 9 11 18 22 33 66 99 198
199 [2] ──► [prime] 1 199
200 [12] ──► 1 2 4 5 8 10 20 25 40 50 100 200
46 primes were found.
Alternate Version
<lang REXX>/* REXX ***************************************************************
- Program to calculate and show divisors of positive integer(s).
- 03.08.2012 Walter Pachl simplified the above somewhat
- in particular I see no benefit from divAdd procedure
- 04.08.2012 the reference to 'above' is no longer valid since that
- was meanwhile changed for the better.
- 04.08.2012 took over some improvements from new above
- /
Parse arg low high . Select
When low= Then Parse Value '1 200' with low high When high= Then high=low Otherwise Nop End
do j=low to high
say ' n = ' right(j,6) " divisors = " divs(j) end
exit
divs: procedure; parse arg x
if x==1 then return 1 /*handle special case of 1 */
Parse Value '1' x With lo hi /*initialize lists: lo=1 hi=x */
odd=x//2 /* 1 if x is odd */
Do j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */</lang>
- output when using the default input:
(Shown at 3/4 size.)
n = 1 divisors = 1 n = 2 divisors = 1 2 n = 3 divisors = 1 3 n = 4 divisors = 1 2 4 n = 5 divisors = 1 5 n = 6 divisors = 1 2 3 6 n = 7 divisors = 1 7 n = 8 divisors = 1 2 4 8 n = 9 divisors = 1 3 9 n = 10 divisors = 1 2 5 10 n = 11 divisors = 1 11 n = 12 divisors = 1 2 3 4 6 12 n = 13 divisors = 1 13 n = 14 divisors = 1 2 7 14 n = 15 divisors = 1 3 5 15 n = 16 divisors = 1 2 4 8 16 n = 17 divisors = 1 17 n = 18 divisors = 1 2 3 6 9 18 n = 19 divisors = 1 19 n = 20 divisors = 1 2 4 5 10 20 n = 21 divisors = 1 3 7 21 n = 22 divisors = 1 2 11 22 n = 23 divisors = 1 23 n = 24 divisors = 1 2 3 4 6 8 12 24 n = 25 divisors = 1 5 25 n = 26 divisors = 1 2 13 26 n = 27 divisors = 1 3 9 27 n = 28 divisors = 1 2 4 7 14 28 n = 29 divisors = 1 29 n = 30 divisors = 1 2 3 5 6 10 15 30 n = 31 divisors = 1 31 n = 32 divisors = 1 2 4 8 16 32 n = 33 divisors = 1 3 11 33 n = 34 divisors = 1 2 17 34 n = 35 divisors = 1 5 7 35 n = 36 divisors = 1 2 3 4 6 9 12 18 36 n = 37 divisors = 1 37 n = 38 divisors = 1 2 19 38 n = 39 divisors = 1 3 13 39 n = 40 divisors = 1 2 4 5 8 10 20 40 n = 41 divisors = 1 41 n = 42 divisors = 1 2 3 6 7 14 21 42 n = 43 divisors = 1 43 n = 44 divisors = 1 2 4 11 22 44 n = 45 divisors = 1 3 5 9 15 45 n = 46 divisors = 1 2 23 46 n = 47 divisors = 1 47 n = 48 divisors = 1 2 3 4 6 8 12 16 24 48 n = 49 divisors = 1 7 49 n = 50 divisors = 1 2 5 10 25 50 n = 51 divisors = 1 3 17 51 n = 52 divisors = 1 2 4 13 26 52 n = 53 divisors = 1 53 n = 54 divisors = 1 2 3 6 9 18 27 54 n = 55 divisors = 1 5 11 55 n = 56 divisors = 1 2 4 7 8 14 28 56 n = 57 divisors = 1 3 19 57 n = 58 divisors = 1 2 29 58 n = 59 divisors = 1 59 n = 60 divisors = 1 2 3 4 5 6 10 12 15 20 30 60 n = 61 divisors = 1 61 n = 62 divisors = 1 2 31 62 n = 63 divisors = 1 3 7 9 21 63 n = 64 divisors = 1 2 4 8 16 32 64 n = 65 divisors = 1 5 13 65 n = 66 divisors = 1 2 3 6 11 22 33 66 n = 67 divisors = 1 67 n = 68 divisors = 1 2 4 17 34 68 n = 69 divisors = 1 3 23 69 n = 70 divisors = 1 2 5 7 10 14 35 70 n = 71 divisors = 1 71 n = 72 divisors = 1 2 3 4 6 8 9 12 18 24 36 72 n = 73 divisors = 1 73 n = 74 divisors = 1 2 37 74 n = 75 divisors = 1 3 5 15 25 75 n = 76 divisors = 1 2 4 19 38 76 n = 77 divisors = 1 7 11 77 n = 78 divisors = 1 2 3 6 13 26 39 78 n = 79 divisors = 1 79 n = 80 divisors = 1 2 4 5 8 10 16 20 40 80 n = 81 divisors = 1 3 9 27 81 n = 82 divisors = 1 2 41 82 n = 83 divisors = 1 83 n = 84 divisors = 1 2 3 4 6 7 12 14 21 28 42 84 n = 85 divisors = 1 5 17 85 n = 86 divisors = 1 2 43 86 n = 87 divisors = 1 3 29 87 n = 88 divisors = 1 2 4 8 11 22 44 88 n = 89 divisors = 1 89 n = 90 divisors = 1 2 3 5 6 9 10 15 18 30 45 90 n = 91 divisors = 1 7 13 91 n = 92 divisors = 1 2 4 23 46 92 n = 93 divisors = 1 3 31 93 n = 94 divisors = 1 2 47 94 n = 95 divisors = 1 5 19 95 n = 96 divisors = 1 2 3 4 6 8 12 16 24 32 48 96 n = 97 divisors = 1 97 n = 98 divisors = 1 2 7 14 49 98 n = 99 divisors = 1 3 9 11 33 99 n = 100 divisors = 1 2 4 5 10 20 25 50 100 n = 101 divisors = 1 101 n = 102 divisors = 1 2 3 6 17 34 51 102 n = 103 divisors = 1 103 n = 104 divisors = 1 2 4 8 13 26 52 104 n = 105 divisors = 1 3 5 7 15 21 35 105 n = 106 divisors = 1 2 53 106 n = 107 divisors = 1 107 n = 108 divisors = 1 2 3 4 6 9 12 18 27 36 54 108 n = 109 divisors = 1 109 n = 110 divisors = 1 2 5 10 11 22 55 110 n = 111 divisors = 1 3 37 111 n = 112 divisors = 1 2 4 7 8 14 16 28 56 112 n = 113 divisors = 1 113 n = 114 divisors = 1 2 3 6 19 38 57 114 n = 115 divisors = 1 5 23 115 n = 116 divisors = 1 2 4 29 58 116 n = 117 divisors = 1 3 9 13 39 117 n = 118 divisors = 1 2 59 118 n = 119 divisors = 1 7 17 119 n = 120 divisors = 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 n = 121 divisors = 1 11 121 n = 122 divisors = 1 2 61 122 n = 123 divisors = 1 3 41 123 n = 124 divisors = 1 2 4 31 62 124 n = 125 divisors = 1 5 25 125 n = 126 divisors = 1 2 3 6 7 9 14 18 21 42 63 126 n = 127 divisors = 1 127 n = 128 divisors = 1 2 4 8 16 32 64 128 n = 129 divisors = 1 3 43 129 n = 130 divisors = 1 2 5 10 13 26 65 130 n = 131 divisors = 1 131 n = 132 divisors = 1 2 3 4 6 11 12 22 33 44 66 132 n = 133 divisors = 1 7 19 133 n = 134 divisors = 1 2 67 134 n = 135 divisors = 1 3 5 9 15 27 45 135 n = 136 divisors = 1 2 4 8 17 34 68 136 n = 137 divisors = 1 137 n = 138 divisors = 1 2 3 6 23 46 69 138 n = 139 divisors = 1 139 n = 140 divisors = 1 2 4 5 7 10 14 20 28 35 70 140 n = 141 divisors = 1 3 47 141 n = 142 divisors = 1 2 71 142 n = 143 divisors = 1 11 13 143 n = 144 divisors = 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 n = 145 divisors = 1 5 29 145 n = 146 divisors = 1 2 73 146 n = 147 divisors = 1 3 7 21 49 147 n = 148 divisors = 1 2 4 37 74 148 n = 149 divisors = 1 149 n = 150 divisors = 1 2 3 5 6 10 15 25 30 50 75 150 n = 151 divisors = 1 151 n = 152 divisors = 1 2 4 8 19 38 76 152 n = 153 divisors = 1 3 9 17 51 153 n = 154 divisors = 1 2 7 11 14 22 77 154 n = 155 divisors = 1 5 31 155 n = 156 divisors = 1 2 3 4 6 12 13 26 39 52 78 156 n = 157 divisors = 1 157 n = 158 divisors = 1 2 79 158 n = 159 divisors = 1 3 53 159 n = 160 divisors = 1 2 4 5 8 10 16 20 32 40 80 160 n = 161 divisors = 1 7 23 161 n = 162 divisors = 1 2 3 6 9 18 27 54 81 162 n = 163 divisors = 1 163 n = 164 divisors = 1 2 4 41 82 164 n = 165 divisors = 1 3 5 11 15 33 55 165 n = 166 divisors = 1 2 83 166 n = 167 divisors = 1 167 n = 168 divisors = 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 n = 169 divisors = 1 13 169 n = 170 divisors = 1 2 5 10 17 34 85 170 n = 171 divisors = 1 3 9 19 57 171 n = 172 divisors = 1 2 4 43 86 172 n = 173 divisors = 1 173 n = 174 divisors = 1 2 3 6 29 58 87 174 n = 175 divisors = 1 5 7 25 35 175 n = 176 divisors = 1 2 4 8 11 16 22 44 88 176 n = 177 divisors = 1 3 59 177 n = 178 divisors = 1 2 89 178 n = 179 divisors = 1 179 n = 180 divisors = 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 n = 181 divisors = 1 181 n = 182 divisors = 1 2 7 13 14 26 91 182 n = 183 divisors = 1 3 61 183 n = 184 divisors = 1 2 4 8 23 46 92 184 n = 185 divisors = 1 5 37 185 n = 186 divisors = 1 2 3 6 31 62 93 186 n = 187 divisors = 1 11 17 187 n = 188 divisors = 1 2 4 47 94 188 n = 189 divisors = 1 3 7 9 21 27 63 189 n = 190 divisors = 1 2 5 10 19 38 95 190 n = 191 divisors = 1 191 n = 192 divisors = 1 2 3 4 6 8 12 16 24 32 48 64 96 192 n = 193 divisors = 1 193 n = 194 divisors = 1 2 97 194 n = 195 divisors = 1 3 5 13 15 39 65 195 n = 196 divisors = 1 2 4 7 14 28 49 98 196 n = 197 divisors = 1 197 n = 198 divisors = 1 2 3 6 9 11 18 22 33 66 99 198 n = 199 divisors = 1 199 n = 200 divisors = 1 2 4 5 8 10 20 25 40 50 100 200
Ring
<lang ring> nArray = list(100) n = 45 j = 0 for i = 1 to n
if n % i = 0 j = j + 1 nArray[j] = i ok
next
see "Factors of " + n + " = " for i = 1 to j
see "" + nArray[i] + " "
next </lang>
Ruby
<lang ruby>class Integer
def factors() (1..self).select { |n| (self % n).zero? } end
end p 45.factors</lang>
[1, 3, 5, 9, 15, 45]
As we only have to loop up to , we can write <lang ruby>class Integer
def factors
1.upto(Integer.sqrt(self)).select {|i| (self % i).zero?}.inject([]) do |f, i|
f << self/i unless i == self/i
f << i
end.sort
end
end [45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}</lang>
- Output:
45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64]
Using the prime library
<lang ruby> require 'prime'
def factors m
return [1] if 1==m
primes, powers = Prime.prime_division(m).transpose
ranges = powers.map{|n| (0..n).to_a}
ranges[0].product( *ranges[1..-1] ).
map{|es| primes.zip(es).map{|p,e| p**e}.reduce :*}.
sort
end
[1, 7, 45, 100].each{|n| p factors n} </lang> Output:
[1] [1, 7] [1, 3, 5, 9, 15, 45] [1, 2, 4, 5, 10, 20, 25, 50, 100]
Run BASIC
<lang runbasic>PRINT "Factors of 45 are ";factorlist$(45) PRINT "Factors of 12345 are "; factorlist$(12345) END
function factorlist$(f) DIM L(100) FOR i = 1 TO SQR(f)
IF (f MOD i) = 0 THEN
L(c) = i
c = c + 1
IF (f <> i^2) THEN
L(c) = (f / i)
c = c + 1
END IF
END IF
NEXT i s = 1 while s = 1 s = 0 for i = 0 to c-1
if L(i) > L(i+1) and L(i+1) <> 0 then t = L(i) L(i) = L(i+1) L(i+1) = t s = 1 end if
next i wend FOR i = 0 TO c-1
factorlist$ = factorlist$ + STR$(L(i)) + ", "
NEXT end function</lang>
- Output:
Factors of 45 are 1, 3, 5, 9, 15, 45, Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345,
Rust
<lang rust>fn main() {
assert_eq!(vec![1, 2, 4, 5, 10, 10, 20, 25, 50, 100], factor(100)); // asserts that two expressions are equal to each other assert_eq!(vec![1, 101], factor(101));
}
fn factor(num: i32) -> Vec<i32> {
let mut factors: Vec<i32> = Vec::new(); // creates a new vector for the factors of the number
for i in 1..((num as f32).sqrt() as i32 + 1) {
if num % i == 0 {
factors.push(i); // pushes smallest factor to factors
factors.push(num/i); // pushes largest factor to factors
}
}
factors.sort(); // sorts the factors into numerical order for viewing purposes
factors // returns the factors
}</lang>
Alternative functional version:
<lang rust> fn factor(n: i32) -> Vec<i32> {
(1..=n).filter(|i| n % i == 0).collect()
} </lang>
Sather
<lang sather>class MAIN is
factors!(n :INT):INT is
yield 1;
loop i ::= 2.upto!( n.flt.sqrt.int );
if n%i = 0 then
yield i;
if (i*i) /= n then
yield n / i;
end;
end;
end;
yield n;
end;
main is
a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|;
loop l ::= a.elt!;
#OUT + "factors of " + l + ": ";
loop ri ::= factors!(l);
#OUT + ri + " ";
end;
#OUT + "\n";
end;
end;
end; </lang>
Scala
Brute force approach: <lang Scala>def factors(num: Int) = {
(1 to num).filter { divisor =>
num % divisor == 0
}
}</lang> Since factors can't be higher than sqrt(num), the code above can be edited as follows <lang Scala>def factors(num: Int) = {
(1 to sqrt(num)).filter { divisor =>
num % divisor == 0
}
}</lang>
Scheme
This implementation uses a naive trial division algorithm. <lang scheme>(define (factors n)
(define (*factors d)
(cond ((> d n) (list))
((= (modulo n d) 0) (cons d (*factors (+ d 1))))
(else (*factors (+ d 1)))))
(*factors 1))
(display (factors 1111111)) (newline)</lang>
- Output:
(1 239 4649 1111111)
Seed7
<lang seed7>$ include "seed7_05.s7i";
const proc: writeFactors (in integer: number) is func
local
var integer: testNum is 0;
begin
write("Factors of " <& number <& ": ");
for testNum range 1 to sqrt(number) do
if number rem testNum = 0 then
if testNum <> 1 then
write(", ");
end if;
write(testNum);
if testNum <> number div testNum then
write(", " <& number div testNum);
end if;
end if;
end for;
writeln;
end func;
const proc: main is func
local
const array integer: numsToFactor is [] (45, 53, 64);
var integer: number is 0;
begin
for number range numsToFactor do
writeFactors(number);
end for;
end func;</lang>
- Output:
Factors of 45: 1, 45, 3, 15, 5, 9 Factors of 53: 1, 53 Factors of 64: 1, 64, 2, 32, 4, 16, 8
SequenceL
Brute Force Method
A simple brute force method using an indexed partial function as a filter. <lang sequencel>Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num;</lang>
Slightly More Efficient Method
A slightly more efficient method, only going up to the sqrt(n). <lang sequencel>Factors(num(0)) := let factorPairs[i] := [i] when i = sqrt(num) else [i, num/i] when num mod i = 0 foreach i within 1 ... floor(sqrt(num)); in join(factorPairs);</lang>
Sidef
Built-in: <lang ruby>say divisors(97) #=> [1, 97] say divisors(2695) #=> [1, 5, 7, 11, 35, 49, 55, 77, 245, 385, 539, 2695]</lang>
Trial-division (slow for large n):
<lang ruby>func divisors(n) {
gather {
{ |d|
take(d, n//d) if d.divides(n)
} << 1..n.isqrt
}.sort.uniq
} [53, 64, 32766].each {|n|
say "divisors(#{n}): #{divisors(n)}"
}</lang>
- Output:
divisors(53): [1, 53] divisors(64): [1, 2, 4, 8, 16, 32, 64] divisors(32766): [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766]
Slate
<lang slate>n@(Integer traits) primeFactors [
[| :result |
result nextPut: 1.
n primesDo: [| :prime | result nextPut: prime]] writingAs: {}
].</lang> where primesDo: is a part of the standard numerics library: <lang slate>n@(Integer traits) primesDo: block "Decomposes the Integer into primes, applying the block to each (in increasing order)." [| div next remaining |
div: 2.
next: 3.
remaining: n.
[[(remaining \\ div) isZero]
whileTrue:
[block applyTo: {div}.
remaining: remaining // div].
remaining = 1] whileFalse:
[div: next.
next: next + 2] "Just looks at the next odd integer."
].</lang>
Smalltalk
Copied from the Python example, but code added to the Integer built in class:
<lang smalltalk>Integer>>factors | a | a := OrderedCollection new. 1 to: (self / 2) do: [ :i | ((self \\ i) = 0) ifTrue: [ a add: i ] ]. a add: self. ^a</lang>
Then use as follows:
<lang smalltalk> 59 factors -> an OrderedCollection(1 59) 120 factors -> an OrderedCollection(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120) </lang>
Standard ML
Need to print the list because Standard ML truncates the display of longer returned lists. <lang Standard ML>fun printIntList ls =
( List.app (fn n => print(Int.toString n ^ " ")) ls; print "\n" );
fun factors n =
let
fun factors'(n, k) =
if k > n then
[]
else if n mod k = 0 then
k :: factors'(n, k+1)
else
factors'(n, k+1)
in
factors'(n,1)
end;
</lang> Call: <lang Standard ML>printIntList(factors 12345) printIntList(factors 120)</lang>
- Output:
1 3 5 15 823 2469 4115 12345 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60
Swift
Simple implementation: <lang Swift>func factors(n: Int) -> [Int] {
return filter(1...n) { n % $0 == 0 }
}</lang> More efficient implementation: <lang Swift>import func Darwin.sqrt
func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) }
func factors(n: Int) -> [Int] {
var result = [Int]()
for factor in filter (1...sqrt(n), { n % $0 == 0 }) {
result.append(factor)
if n/factor != factor { result.append(n/factor) }
}
return sorted(result)
}</lang> Call: <lang Swift>println(factors(4)) println(factors(1)) println(factors(25)) println(factors(63)) println(factors(19)) println(factors(768))</lang>
- Output:
[1, 2, 4] [1] [1, 5, 25] [1, 3, 7, 9, 21, 63] [1, 19] [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]
Tailspin
<lang tailspin> [1..351 -> \(when <?(351 mod $ <=0>)> do $! \)] -> !OUT::write </lang>
- Output:
[1, 3, 9, 13, 27, 39, 117, 351]
Tcl
<lang tcl>proc factors {n} {
set factors {}
for {set i 1} {$i <= sqrt($n)} {incr i} {
if {$n % $i == 0} {
lappend factors $i [expr {$n / $i}]
}
}
return [lsort -unique -integer $factors]
} puts [factors 64] puts [factors 45] puts [factors 53]</lang>
- Output:
1 2 4 8 16 32 64 1 3 5 9 15 45 1 53
UNIX Shell
This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc.
<lang>factor() {
r=`echo "sqrt($1)" | bc` # or `echo $1 v p | dc`
i=1
while [ $i -lt $r ]; do
if [ `expr $1 % $i` -eq 0 ]; then
echo $i
expr $1 / $i
fi
i=`expr $i + 1`
done | sort -nu
} </lang>
Ursa
This program takes an integer from the command line and outputs its factors. <lang ursa>decl int n set n (int args<1>)
decl int i for (set i 1) (< i (+ (/ n 2) 1)) (inc i)
if (= (mod n i) 0)
out i " " console
end if
end for out n endl console</lang>
Ursala
The simple way: <lang Ursala>#import std
- import nat
factors "n" = (filter not remainder/"n") nrange(1,"n")</lang>
The complicated way:
<lang Ursala>factors "n" = nleq-<&@s <.~&r,quotient>*= "n"-* (not remainder/"n")*~ nrange(1,root("n",2))</lang>
Another idea would be to approximate an upper bound for the square root of "n" with some bit twiddling such as &!*K31 "n", which evaluates to a binary number of all 1's half the width of "n" rounded up, and another would be to use the division function to get the quotient and remainder at the same time. Combining these ideas, losing the dummy variable, and cleaning up some other cruft, we have
<lang Ursala>factors = nleq-<&@rrZPFLs+ ^(~&r,division)^*D/~& nrange/1+ &!*K31</lang>
where nleq-<& isn't strictly necessary unless an ordered list is required.
<lang Ursala>#cast %nL
example = factors 100</lang>
- Output:
<1,2,4,5,10,20,25,50,100>
VBA
<lang vb>Function Factors(x As Integer) As String
Application.Volatile Dim i As Integer Dim cooresponding_factors As String Factors = 1 corresponding_factors = x For i = 2 To Sqr(x) If x Mod i = 0 Then Factors = Factors & ", " & i If i <> x / i Then corresponding_factors = x / i & ", " & corresponding_factors End If Next i If x <> 1 Then Factors = Factors & ", " & corresponding_factors
End Function</lang>
- Output:
cell formula is "=Factors(840)" resultant value is "1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840"
Verilog
<lang Verilog> module main;
integer i, n;
initial begin n = 45; $write(n, " =>"); for(i = 1; i <= n / 2; i = i + 1) if(n % i == 0) $write(i); $display(n); $finish ; end
endmodule </lang>
- Output:
45 => 1 3 5 9 15 45
Wortel
<lang wortel>@let {
factors1 &n !-\%%n @to n factors_tacit @(\\%% !- @to) [[ !factors1 10 !factors_tacit 100 !factors1 720 ]]
}</lang>
Returns:
[ [1 2 5 10] [1 2 4 5 10 20 25 50 100] [1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720] ]
Wren
<lang ecmascript>import "/fmt" for Fmt import "/math" for Int
var a = [11, 21, 32, 45, 67, 96, 159, 723, 1024, 5673, 12345, 32767, 123459, 999997] System.print("The factors of the following numbers are:") for (e in a) System.print("%(Fmt.d(6, e)) => %(Int.divisors(e))")</lang>
- Output:
The factors of the following numbers are:
11 => [1, 11]
21 => [1, 3, 7, 21]
32 => [1, 2, 4, 8, 16, 32]
45 => [1, 3, 5, 9, 15, 45]
67 => [1, 67]
96 => [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]
159 => [1, 3, 53, 159]
723 => [1, 3, 241, 723]
1024 => [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
5673 => [1, 3, 31, 61, 93, 183, 1891, 5673]
12345 => [1, 3, 5, 15, 823, 2469, 4115, 12345]
32767 => [1, 7, 31, 151, 217, 1057, 4681, 32767]
123459 => [1, 3, 7, 21, 5879, 17637, 41153, 123459]
999997 => [1, 757, 1321, 999997]
X86 Assembly
<lang asm> section .bss
factorArr resd 250 ;big buffer against seg fault
section .text global _main _main:
mov ebp, esp; for correct debugging
mov eax, 0x7ffffffe ;number of which we want to know the factors, max num this program works with
mov ebx, eax ;save eax
mov ecx, 1 ;n, factor we test for
mov [factorArr], dword 0
looping:
mov eax, ebx ;restore eax
xor edx, edx ;clear edx
div ecx
cmp edx, 0 ;test if our number % n == 0
jne next
mov edx, [factorArr] ;if yes, we increment the size of the array and append n
inc edx
mov [factorArr+edx*4], ecx ;appending n
mov [factorArr], edx ;storing the new size
next:
mov eax, ecx
cmp eax, ebx ;is n bigger then our number ?
jg end ;if yes we end
inc ecx
jmp looping
end:
mov ecx, factorArr ;pass arr address by ecx
xor eax, eax ;clear eax
mov esp, ebp ;garbage collecting
ret
</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; int N0, N, F; [N0:= 1; repeat IntOut(0, N0); Text(0, " = ");
F:= 2; N:= N0;
repeat if rem(N/F) = 0 then
[if N # N0 then Text(0, " * ");
IntOut(0, F);
N:= N/F;
]
else F:= F+1;
until F>N;
if N0=1 then IntOut(0, 1); \1 = 1
CrLf(0);
N0:= N0+1;
until KeyHit; ]</lang>
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 12 = 2 * 2 * 3 13 = 13 14 = 2 * 7 15 = 3 * 5 16 = 2 * 2 * 2 * 2 17 = 17 18 = 2 * 3 * 3 . . . 57086 = 2 * 17 * 23 * 73 57087 = 3 * 3 * 6343 57088 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 223 57089 = 57089 57090 = 2 * 3 * 5 * 11 * 173 57091 = 37 * 1543 57092 = 2 * 2 * 7 * 2039 57093 = 3 * 19031 57094 = 2 * 28547 57095 = 5 * 19 * 601 57096 = 2 * 2 * 2 * 3 * 3 * 13 * 61 57097 = 57097
Yabasic
<lang yabasic> sub printFactors(n)
if n < 1 then return 0 : fi
print n, " =>",
for i = 1 to n / 2
if mod(n, i) = 0 then print i, " "; : fi
next i
print n
end sub
printFactors(11) printFactors(21) printFactors(32) printFactors(45) printFactors(67) printFactors(96) print end </lang>
- Output:
Igual que la entrada de FreeBASIC.
zkl
<lang zkl>fcn f(n){ (1).pump(n.toFloat().sqrt(), List,
'wrap(m){((n % m)==0) and T(m,n/m) or Void.Skip}) }
fcn g(n){ [[(m); [1..n.toFloat().sqrt()],'{n%m==0}; '{T(m,n/m)} ]] } // list comprehension</lang>
- Output:
zkl: f(45) L(L(1,45),L(3,15),L(5,9)) zkl: g(45) L(L(1,45),L(3,15),L(5,9))
ZX Spectrum Basic
<lang zxbasic>10 INPUT "Enter a number or 0 to exit: ";n 20 IF n=0 THEN STOP 30 PRINT "Factors of ";n;": "; 40 FOR i=1 TO n 50 IF FN m(n,i)=0 THEN PRINT i;" "; 60 NEXT i 70 DEF FN m(a,b)=a-INT (a/b)*b</lang>
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