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In this tutorial, we will see how to count trailing zeros in factorial of a number in java.

## Problem

Count number of zeros in factorial of number in java.

**For example:**

Factorial of 6 is 720, so a number of trailing zeros is 1.

Factorial of 14 is 87 178 291 200, so a number of trailing zeros is 2.

## Solution

A very simple approach is to compute the factorial and divide it by 10 to count a number of trailing zeros but bound of ints will be reached very quickly with solution.

Trailing zeroes are created by multiple of 10 and multiples of 10 are created by 5 and 2. As multiple of 2 will always more than multiple of 5, we can simply count the multiples of 5.

Let’s create a simple program to count factorial Trailing Zeroes in java.

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package org.arpit.java2blog.algorithm; public class FactorialTrailingZeroMain { public static void main(String[] args) { FactorialTrailingZeroMain ftzm=new FactorialTrailingZeroMain(); int countFactorialTrailingZeros = ftzm.countFactorialTrailingZeros(29); System.out.println("Factorial trailing zeroes for 29: "+countFactorialTrailingZeros); } public int countFactorialTrailingZeros(int num) { int countOfZeros=0; for(int i=2;i<=num;i++) { countOfZeros+=countFactorsOf5(i); } return countOfZeros; } private int countFactorsOf5(int i) { int count=0; while(i%5==0) { count++; i/=5; } return count; } } |

When you run above program, you will see below output.

This approach works but can we do better?

Yes,we can.

## Algorithms to Count number of zeros in factorial of number in java

- Divide the number by 5 and count the number of multiple of 5.
- Divide the number by 25 and count the number of multiple of 25.
- Divide the number by 125 and count the number of multiple of 125.
- Divide the number by 125 and count the number of multiple of 625 and so on …

## Program for Counting Factorial Trailing Zeroes in java

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package org.arpit.java2blog.algorithm; public class FactorialTrailingZeroMain { public static void main(String[] args) { FactorialTrailingZeroMain ftzm=new FactorialTrailingZeroMain(); int countFactorialTrailingZeros = ftzm.countFactorialTrailingZeros(29); System.out.println("Factorial trailing zeroes for 29: "+countFactorialTrailingZeros); } public int countFactorialTrailingZeros(int num) { int countOfZeros=0; if(num<0) return -1; for(int i=5;num/i>0;i*=5) { countOfZeros+=num/i; } return countOfZeros; } } |

That’s all about counting Factorial Trailing Zeroes in java.

For more programs, refer to data structure and algorithms interview questions in java.