Find all the divisors from a given number

divisors.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Created on Wed Oct 30 10:55:51 2013
# By Danilo J. S. Bellini
# Based on https://gist.github.com/anonymous/7123189
"""
Find all the divisors from a given number
"""

# Ensure compatibility in both Python 2 and 3
from __future__ import division, print_function, unicode_literals
import sys
if sys.version_info.major == 2:
  input = raw_input
  INT_TYPES = (int, getattr(sys.modules["__builtin__"], "long", None))
else: # Python 3
  INT_TYPES = (int,)


from itertools import count, takewhile


def prime_gen():
  """ Prime number generator """
  yield 2
  primes = [] # From now on, there's only odd numbers to care about
  for value in count(start=3, step=2):
    iter_primes = takewhile(lambda x: x * x <= value, primes)
    if all(value % p != 0 for p in iter_primes):
      primes.append(value)
      yield value


def divisors(n):
  """ Sorted divisors generator for a given number besides 1, with repeats """
  if not isinstance(n, INT_TYPES):
    raise TypeError("Input have to be an integer.")
  if n <= 0:
    raise ValueError("Given input isn't positive.")

  remain = n
  for p in prime_gen():
    if remain == 1:
      break
    while remain % p == 0:
      remain //= p
      yield p


if __name__ == "__main__":
  n = int(input("Type in a positive integer number: "))
  size = len(str(n))
  for d in divisors(n):
    print("{n:{size}} | {d}".format(**locals()))
    n //= d
  print("{n:{size}} | -".format(**locals()))

prime_comparison.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Created on Tue Dec 03 16:27:04 2013
# By Danilo J. S. Bellini
"""
Prime number generation duration comparison
"""

from __future__ import print_function, unicode_literals

from itertools import count, takewhile
from collections import deque
from time import time

def prime_gen_list():
  """ Prime number generator using a list for internal storage """
  yield 2
  primes = [] # From now on, there's only odd numbers to care about
  for value in count(start=3, step=2):
    iter_primes = takewhile(lambda x: x * x <= value, primes)
    if all(value % p != 0 for p in iter_primes):
      primes.append(value)
      yield value

def prime_gen_deque():
  """ Prime number generator using a deque for internal storage """
  yield 2
  primes = deque()
  for value in count(start=3, step=2):
    iter_primes = takewhile(lambda x: x * x <= value, primes)
    if all(value % p != 0 for p in iter_primes):
      primes.append(value)
      yield value

duration = 10 * 60 # seconds

start = time()
for p in prime_gen_list():
  if time() - start > duration:
    break
  prime_list = p

start = time()
for p in prime_gen_deque():
  if time() - start > duration:
    break
  prime_deque = p

print("Duration (for each generator):", duration, "seconds")
print("Prime found with a list for storage:", prime_list)
print("Prime found with a deque for storage:", prime_deque)