Counting trailing zeros of numbers resulted from factorial

Question

I\'m trying to count trailing zeros of numbers that are resulted from factorials (meaning that the numbers get quite large). Following code takes a number, compute the facto

Answer 1

Your task is not to compute the factorial but the number of zeroes. A good solution uses the formula from http://en.wikipedia.org/wiki/Trailing_zeros (which you can try to prove)

def zeroes(n):
    i = 1
    result = 0
    while n >= i:
        i *= 5
        result += n/i  # (taking floor, just like Python or Java does)
    return result

Hope you can translate this to Java. This simply computes [n / 5] + [n / 25] + [n / 125] + [n / 625] + ... and stops when the divisor gets larger than n.

DON'T use BigIntegers. This is a bozosort. Such solutions require seconds of time for large numbers.