# find all multiplicands and multipliers for a number

Marko Rauhamaa marko at pacujo.net
Sat Apr 11 09:14:39 CEST 2015

```Paul Rubin <no.email at nospam.invalid>:

> This takes about 4 seconds on a Intel(R) Core(TM) i5-3230M CPU @ 2.60GHz
> laptop (64 bit linux):

Converted to Python3:
========================================================================
#!/usr/bin/env python3

import itertools, time

def candidates():
yield 2
yield 3
for i in itertools.count(5,6):
yield i
yield i+2

def fac(n):
for c in candidates():
if c*c > n:
yield n
break
while n%c == 0:
yield c
n //= c

t0 = time.time()
print(list(fac(2**111+1)))
print(time.time() - t0)
========================================================================

This is slightly faster:

========================================================================
#!/usr/bin/env python3

import time

def fac(n):
for c in range(n):
if c*c > n:
yield n
break
while n%c == 0:
yield c
n //= c

t0 = time.time()
print(list(fac(2**111+1)))
print(time.time() - t0)
========================================================================

Marko

```