Kata

The factorial function is defined as follows:

0! = 1
n! = 1 * 2 * 3 * 4 * ... * n-2 * n-1 * n

Usually, the factorials of large numbers will have trailing zeroes. Your task is to create a function which returns the number of trailing zeroes of num! in a given base.

Here's two examples to get you started:

(num = 15, base = 10) => 3
# 15! = 1307674368000, which has 3 trailing 0's

(num = 7, base = 2) => 4
# 7! = 5040 = 0b1001110110000, which has 4 trailing 0's

Your code should be able to handle some very large numbers.

Note:

• num >= 0
• base >= 2

HINT: Should you not make any headway after trying a long time, you should try this kata first.