Divisors of a natural number
Create a program to generate all the divisors of a given natural number.
Use it to generate and show here all the divisors of the numbers 2**(n-1) for n in the (inclusive) range [1, 16] and also for n = 31
Awk
<lang awk># Implemented by Arjun Sunel awk 'func divisors(n){printf "divisors of ";print n;printf " = [";for(j=1;j<n;j++){if(n%j==0){printf j;printf ","}};printf n;printf "]\n";}BEGIN{for(i=1;i<=16;i++)divisors((2^(i-1)) ); divisors(2^(31-1))}' </lang>
- Output:
divisors of 1 = [1] divisors of 2 = [1,2] divisors of 4 = [1,2,4] divisors of 8 = [1,2,4,8] divisors of 16 = [1,2,4,8,16] divisors of 32 = [1,2,4,8,16,32] divisors of 64 = [1,2,4,8,16,32,64] divisors of 128 = [1,2,4,8,16,32,64,128] divisors of 256 = [1,2,4,8,16,32,64,128,256] divisors of 512 = [1,2,4,8,16,32,64,128,256,512] divisors of 1024 = [1,2,4,8,16,32,64,128,256,512,1024] divisors of 2048 = [1,2,4,8,16,32,64,128,256,512,1024,2048] divisors of 4096 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096] divisors of 8192 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192] divisors of 16384 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384] divisors of 32768 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768] divisors of 1073741824 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]
C
<lang c>// Implemented by Arjun Sunel
- include<stdio.h>
- include<math.h>
int divisors(int n) { int i, j; printf("divisors(%d) = [",n); for (i=1;i<n;i++) { if (n%i==0) printf("%d,",i);
} printf("%d]\n",i); }
int main() { int n,i;
for (i=1 ; i<=16;i++) { divisors(pow(2,i-1)); } divisors(pow(2,31-1)); return 0; }</lang>
- Output:
divisors(1) = [1] divisors(2) = [1,2] divisors(4) = [1,2,4] divisors(8) = [1,2,4,8] divisors(16) = [1,2,4,8,16] divisors(32) = [1,2,4,8,16,32] divisors(64) = [1,2,4,8,16,32,64] divisors(128) = [1,2,4,8,16,32,64,128] divisors(256) = [1,2,4,8,16,32,64,128,256] divisors(512) = [1,2,4,8,16,32,64,128,256,512] divisors(1024) = [1,2,4,8,16,32,64,128,256,512,1024] divisors(2048) = [1,2,4,8,16,32,64,128,256,512,1024,2048] divisors(4096) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096] divisors(8192) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192] divisors(16384) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384] divisors(32768) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768] divisors(1073741824) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]
C++
<lang cpp>// Implemented by Arjun Sunel
- include<iostream>
- include<cmath>
using namespace std;
int divisors(int n) { int i, j; cout<<"divisors("<<n<<") = ["; for (i=1;i<n;i++) { if (n%i==0) cout <<i<<",";
} cout<<n<<"]"<<endl; }
int main() { int n,i;
for (i=1 ; i<=16;i++) { divisors(pow(2,i-1)); } divisors(pow(2,31-1)); return 0; } </lang>
- Output:
divisors(1) = [1] divisors(2) = [1,2] divisors(4) = [1,2,4] divisors(8) = [1,2,4,8] divisors(16) = [1,2,4,8,16] divisors(32) = [1,2,4,8,16,32] divisors(64) = [1,2,4,8,16,32,64] divisors(128) = [1,2,4,8,16,32,64,128] divisors(256) = [1,2,4,8,16,32,64,128,256] divisors(512) = [1,2,4,8,16,32,64,128,256,512] divisors(1024) = [1,2,4,8,16,32,64,128,256,512,1024] divisors(2048) = [1,2,4,8,16,32,64,128,256,512,1024,2048] divisors(4096) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096] divisors(8192) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192] divisors(16384) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384] divisors(32768) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768] divisors(1073741824) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]
Java
<lang java>// Implemented by Arjun Sunel
public class divisors { static void ans(double a) { System.out.print("divisors of " +(int)a + " = ["); for(int i = 1; i < a; i = i+1) { if (a % i == 0) { System.out.print(i + ","); } } System.out.print((int)a); System.out.println("]"); }
public static void main(String args[]) { for(int x = 1; x <= 16; x = x+1) { ans(Math.pow(2, x-1)); } ans(Math.pow(2, 31-1)); } }</lang>
- Output:
divisors of 1 = [1] divisors of 2 = [1,2] divisors of 4 = [1,2,4] divisors of 8 = [1,2,4,8] divisors of 16 = [1,2,4,8,16] divisors of 32 = [1,2,4,8,16,32] divisors of 64 = [1,2,4,8,16,32,64] divisors of 128 = [1,2,4,8,16,32,64,128] divisors of 256 = [1,2,4,8,16,32,64,128,256] divisors of 512 = [1,2,4,8,16,32,64,128,256,512] divisors of 1024 = [1,2,4,8,16,32,64,128,256,512,1024] divisors of 2048 = [1,2,4,8,16,32,64,128,256,512,1024,2048] divisors of 4096 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096] divisors of 8192 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192] divisors of 16384 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384] divisors of 32768 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768] divisors of 1073741824 = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]
Python
<lang python>import math from operator import mul from itertools import product from functools import reduce
def fac(n):
\
return the prime factors for n
>>> fac(600)
[5, 5, 3, 2, 2, 2]
>>> fac(1000)
[5, 5, 5, 2, 2, 2]
>>>
step = lambda x: 1 + x*4 - (x//2)*2
maxq = int(math.floor(math.sqrt(n)))
d = 1
q = n % 2 == 0 and 2 or 3
while q <= maxq and n % q != 0:
q = step(d)
d += 1
res = []
if q <= maxq:
res.extend(fac(n//q))
res.extend(fac(q))
else: res=[n]
return res
def fact(n):
\ return the prime factors and their multiplicities for n >>> fact(600) [(2, 3), (3, 1), (5, 2)] >>> fact(1000) [(2, 3), (5, 3)] >>> res = fac(n) return [(c, res.count(c)) for c in set(res)]
def divisors(n):
factors = fact(n) # [(primefactor, multiplicity), ...]
primes, maxpowers = zip(*factors)
powerranges = (range(m+1) for m in maxpowers)
powers = product(*powerranges)
return (
reduce(mul,
(prime**power for prime, power in zip(primes, powergroup)),
1)
for powergroup in powers)
if __name__ == '__main__':
for n in list(range(1,17)) + [31]:
tocalc = 2**(n - 1)
print("divisors(%s) = %s" % (tocalc, sorted(divisors(tocalc))))</lang>
- Output:
divisors(1) = [1, 1] divisors(2) = [1, 2] divisors(4) = [1, 2, 4] divisors(8) = [1, 2, 4, 8] divisors(16) = [1, 2, 4, 8, 16] divisors(32) = [1, 2, 4, 8, 16, 32] divisors(64) = [1, 2, 4, 8, 16, 32, 64] divisors(128) = [1, 2, 4, 8, 16, 32, 64, 128] divisors(256) = [1, 2, 4, 8, 16, 32, 64, 128, 256] divisors(512) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] divisors(1024) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024] divisors(2048) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048] divisors(4096) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096] divisors(8192) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192] divisors(16384) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384] divisors(32768) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768] divisors(1073741824) = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824]