number-of-trailing-zeros-of-n.md

Number of trailing zeros of N! ^{5 Kyu}

^{LINK TO THE KATA - ALGORITHMS LOGIC MATHEMATICS}

Description

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...

For more info, see: http://mathworld.wolfram.com/Factorial.html

Examples

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

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

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

Solution

const zeros = n => {
  let zeros = 0

  while (n > 0) {
    n = Math.floor(n / 5)
    zeros += n
  }

  return zeros
}