last-non-zero-factorial-digit

def lznd_trailing_zeros (n):
    "Return the number of trailing zeros of N!"
    r = 0
    for i in range(5, n+1, 5):
        while i%5 == 0:
            r += 1
            i = i / 5
    return r

def lznd_fact (n):
    "Return the last non-zero digit of N!"
    f2 = f5 = lznd_trailing_zeros(n)
    r = 1
    for i in range(1,n+1):
        while f2 > 0 and i%2 == 0:
            f2 -= 1
            i /= 2
        while f5 > 0 and i%5 == 0:
            f5 -= 1
            i /= 5
        r = (i*r) % 10
    return r