#! /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()