Python factorization

Question

I\'d just like to know the best way of listing all integer factors of a number, given a dictionary of its prime factors and their exponents.
For example if we have {2:3

Answer 1

Using itertools.product from Python 2.6:

#!/usr/bin/env python
import itertools, operator

def all_factors(prime_dict):
    series = [[p**e for e in range(maxe+1)] for p, maxe in prime_dict.items()]
    for multipliers in itertools.product(*series):
        yield reduce(operator.mul, multipliers)

Example:

print sorted(all_factors({2:3, 3:2, 5:1}))

Output:

[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60,
 72, 90, 120, 180, 360]