Count Factorial Trailing Zeroes in java

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.

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

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.