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.

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.

Factorial trailing zeroes for 29: 6

This approach works but can we do better?

Yes,we can.

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

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; } }

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