#! /usr/bin/python2.7
# Factorize numbers.
# The algorithm is not efficient, but easy to understand.
# If there are large factors, it will take forever to find them,
# because we try all odd numbers between 3 and sqrt(n)...
import sys
from math import sqrt
def fact(n):
if n < 1:
raise ValueError('fact() argument should be >= 1')
if n == 1:
return [] # special case
res = []
# Treat even factors special, so we can use i += 2 later
while n % 2 == 0:
res.append(2)
n //= 2
# Try odd numbers up to sqrt(n)
limit = sqrt(n+1)
i = 3
while i <= limit:
if n % i == 0:
res.append(i)
n //= i
limit = sqrt(n+1)
else:
i += 2
if n != 1:
res.append(n)
return res
def main():
if len(sys.argv) > 1:
source = sys.argv[1:]
else:
source = iter(raw_input, '')
for arg in source:
try:
n = int(arg)
except ValueError:
print arg, 'is not an integer'
else:
print n, fact(n)
if __name__ == "__main__":
main()