Largest prime factor
- Task
The task description is taken for Project Euler (https://projecteuler.net/problem=3)
What is the largest prime factor of the number 600851475143 ?
BASIC
FreeBASIC
<lang freebasic>#include"isprime.bas" dim as ulongint n = 600851475143, j = 3 while not isprime(n)
if n mod j = 0 then n/=j j+=2
wend print n</lang>
- Output:
6857
GW-BASIC
No primality testing is even required. <lang gwbasic>10 N#=600851475143# 20 J#=3 30 IF J#=N# THEN GOTO 100 40 IF INT(N#/J#) = N#/J# THEN N# = N#/J# 50 J#=J#+2 60 GOTO 30 100 PRINT N#</lang>
- Output:
6857
C
<lang c>#include <stdio.h>
- include <stdlib.h>
int isprime( long int n ) {
int i=3; if(!(n%2)) return 0; while( i*i < n ) { if(!(n%i)) return 0; i+=2; } return 1;
}
int main(void) {
long int n=600851475143, j=3;
while(!isprime(n)) { if(!(n%j)) n/=j; j+=2; } printf( "%ld\n", n ); return 0;
}</lang>
- Output:
6857
Fermat
<lang fermat>n:=600851475143; j:=3; while Isprime(n)<>1 do
if Divides(j, n) then n:=n/j fi; j:=j+2;
od; !!n;</lang>
- Output:
6857
Go
<lang go>package main
import "fmt"
func largestPrimeFactor(n uint64) uint64 {
if n < 2 { return 1 } inc := [8]uint64{4, 2, 4, 2, 4, 6, 2, 6} max := uint64(1) for n%2 == 0 { max = 2 n /= 2 } for n%3 == 0 { max = 3 n /= 3 } for n%5 == 0 { max = 5 n /= 5 } k := uint64(7) i := 0 for k*k <= n { if n%k == 0 { max = k n /= k } else { k += inc[i] i = (i + 1) % 8 } } if n > 1 { return n } return max
}
func main() {
n := uint64(600851475143) fmt.Println("The largest prime factor of", n, "is", largestPrimeFactor(n), "\b.")
}</lang>
- Output:
The largest prime factor of 600851475143 is 6857.
PARI/GP
<lang parigp>A=factor(600851475143) print(A[matsize(A)[1],1])</lang>
- Output:
6857
Raku
Pure Raku, not particularly fast. <lang perl6>use Prime::Factor;
my $start = now;
for flat 600851475143, (1..∞).map: { 2 +< $_ - 1 } {
say "Largest prime factor of $_: ", .&prime-factors.max; exit if now - $start > 1.0; # quit after one second of run time
}</lang>
Largest prime factor of 600851475143: 6857 Largest prime factor of 3: 3 Largest prime factor of 7: 7 Largest prime factor of 15: 5 Largest prime factor of 31: 31 Largest prime factor of 63: 7 Largest prime factor of 127: 127 Largest prime factor of 255: 17 Largest prime factor of 511: 73 Largest prime factor of 1023: 31 Largest prime factor of 2047: 89 Largest prime factor of 4095: 13 Largest prime factor of 8191: 8191 Largest prime factor of 16383: 127 Largest prime factor of 32767: 151 Largest prime factor of 65535: 257 Largest prime factor of 131071: 131071 Largest prime factor of 262143: 73 Largest prime factor of 524287: 524287 Largest prime factor of 1048575: 41 Largest prime factor of 2097151: 337 Largest prime factor of 4194303: 683 Largest prime factor of 8388607: 178481 Largest prime factor of 16777215: 241 Largest prime factor of 33554431: 1801 Largest prime factor of 67108863: 8191 Largest prime factor of 134217727: 262657 Largest prime factor of 268435455: 127 Largest prime factor of 536870911: 2089 Largest prime factor of 1073741823: 331 Largest prime factor of 2147483647: 2147483647 Largest prime factor of 4294967295: 65537 Largest prime factor of 8589934591: 599479 Largest prime factor of 17179869183: 131071 Largest prime factor of 34359738367: 122921 Largest prime factor of 68719476735: 109 Largest prime factor of 137438953471: 616318177 Largest prime factor of 274877906943: 524287 Largest prime factor of 549755813887: 121369 Largest prime factor of 1099511627775: 61681 Largest prime factor of 2199023255551: 164511353 Largest prime factor of 4398046511103: 5419 Largest prime factor of 8796093022207: 2099863 Largest prime factor of 17592186044415: 2113 Largest prime factor of 35184372088831: 23311 Largest prime factor of 70368744177663: 2796203 Largest prime factor of 140737488355327: 13264529 Largest prime factor of 281474976710655: 673 Largest prime factor of 562949953421311: 4432676798593 Largest prime factor of 1125899906842623: 4051 Largest prime factor of 2251799813685247: 131071 Largest prime factor of 4503599627370495: 8191 Largest prime factor of 9007199254740991: 20394401 Largest prime factor of 18014398509481983: 262657 Largest prime factor of 36028797018963967: 201961 Largest prime factor of 72057594037927935: 15790321 Largest prime factor of 144115188075855871: 1212847 Largest prime factor of 288230376151711743: 3033169 Largest prime factor of 576460752303423487: 3203431780337 Largest prime factor of 1152921504606846975: 1321 Largest prime factor of 2305843009213693951: 2305843009213693951 Largest prime factor of 4611686018427387903: 2147483647 Largest prime factor of 9223372036854775807: 649657 Largest prime factor of 18446744073709551615: 6700417 Largest prime factor of 36893488147419103231: 145295143558111 Largest prime factor of 73786976294838206463: 599479 Largest prime factor of 147573952589676412927: 761838257287 Largest prime factor of 295147905179352825855: 131071 Largest prime factor of 590295810358705651711: 10052678938039 Largest prime factor of 1180591620717411303423: 122921 Largest prime factor of 2361183241434822606847: 212885833 Largest prime factor of 4722366482869645213695: 38737 Largest prime factor of 9444732965739290427391: 9361973132609 Largest prime factor of 18889465931478580854783: 616318177 Largest prime factor of 37778931862957161709567: 10567201 Largest prime factor of 75557863725914323419135: 525313 Largest prime factor of 151115727451828646838271: 581283643249112959 Largest prime factor of 302231454903657293676543: 22366891 Largest prime factor of 604462909807314587353087: 1113491139767 Largest prime factor of 1208925819614629174706175: 4278255361 Largest prime factor of 2417851639229258349412351: 97685839 Largest prime factor of 4835703278458516698824703: 8831418697 Largest prime factor of 9671406556917033397649407: 57912614113275649087721 Largest prime factor of 19342813113834066795298815: 14449 Largest prime factor of 38685626227668133590597631: 9520972806333758431 Largest prime factor of 77371252455336267181195263: 2932031007403 Largest prime factor of 154742504910672534362390527: 9857737155463 Largest prime factor of 309485009821345068724781055: 2931542417 Largest prime factor of 618970019642690137449562111: 618970019642690137449562111 Largest prime factor of 1237940039285380274899124223: 18837001 Largest prime factor of 2475880078570760549798248447: 23140471537 Largest prime factor of 4951760157141521099596496895: 2796203 Largest prime factor of 9903520314283042199192993791: 658812288653553079
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "The largest prime factor of the number 600851475143 is:" + nl num = 600851475143 numSqrt = sqrt(num) numSqrt = floor(numSqrt) if numSqrt%2 = 0
numSqrt++
ok
for n = numSqrt to 3 step -2
if isprime(n) and num%n = 0 exit ok
next
see "" + n + nl see "done..." + nl </lang>
- Output:
working... The largest prime factor of the number 600851475143 is: 6857 done...
Wren
Without using any library functions at all (it's a one-liner otherwise): <lang ecmascript>var largestPrimeFactor = Fn.new { |n|
if (!n.isInteger || n < 2) return 1 var inc = [4, 2, 4, 2, 4, 6, 2, 6] var max = 1 while (n%2 == 0) { max = 2 n = (n/2).floor } while (n%3 == 0) { max = 3 n = (n/3).floor } while (n%5 == 0) { max = 5 n = (n/5).floor } var k = 7 var i = 0 while (k * k <= n) { if (n%k == 0) { max = k n = (n/k).floor } else { k = k + inc[i] i = (i + 1) % 8 } } return (n > 1) ? n : max
}
var n = 600851475143 System.print("The largest prime factor of %(n) is %(largestPrimeFactor.call(n)).")</lang>
- Output:
The largest prime factor of 600851475143 is 6857.