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

Yes. When you've got an algorithm that needs n nested for loops, you can usually turn it into a recursive function:

def print_factors(d, product=1):
    if len(d) == 0:      # Base case: we've dealt with all prime factors, so
        print product    # Just print the product
        return
    d2 = dict(d)         # Copy the dict because we don't want to modify it
    k,v = d2.popitem()   # Pick any k**v pair from it
    for i in range(v+1): # For all possible powers i of k from 0 to v (inclusive)
                         # Multiply the product by k**i and recurse.
        print_factors(d2, product*k**i)

d = {2:3, 3:2, 5:1}
print_factors(d)