kyu5_number_of_trailing_zeros_of_N.py

""" Write a program that will calculate the number of trailing zeros in a factorial of a given number;
N! = 1 * 2 * 3 * ... * N
Be careful 1000! has 2568 digits...

Hint: You're not meant to calculate the factorial. Find another way to find the number of zeros;

Examples:
    zeros(6) = 1
    # 6! = 1 * 2 * 3 * 4 * 5 * 6 = 720 --> 1 trailing zero

    zeros(12) = 2
    # 12! = 479001600 --> 2 trailing zeros

"""


def zeros(n):
    count, i = 0, 5
    while n // i:
        count, i = count + n // i, i * 5
    return count