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# Java Program to Find Factorial of a Number Recursively

• Last Updated : 22 Jul, 2021

Factorial of a number n is defined as a product of all positive descending integers, Factorial of n is denoted by n!. Factorial can be calculated using the following recursive formula where the recursive call is made to a multiplicity of all the numbers lesser than the number for which the factorial is computed as the formula to calculate factorial is as follows:

n! = n * [(n-1)!]
i.e factorial of n (n!) = n * (n-1) * ......* 3 * 2* 1

Note: Factorial of 0 is 1

Illustration:

Input      : 5!
Processing : 5*4*3*2*1
Output     : 120
Input      : 6!
Processing : 6*5*4*3*2*1
Output     : 720

Example 1:

## Java

 // Java Program to Find Factorial of a Number// where N>=0 is currently N>1 // Importing input output classesimport java.io.*;// importing utiltity classesimport java.util.*; // Main classclass GFG {     // Method 1    // To calculate factorial    static int factorial(int n)    {         // Handling base case        // iIf value of n=1 or n=0, it returns 1        if (n == 0 || n == 1)            return 1;         // Generic case        // Otherwise we do n*(n-1)!        return n * factorial(n - 1);    }     // Method 2    // main driver method    public static void main(String[] args)    {         // Calling method 1 to compute factorial and        // storing the result into a variable        int ans = factorial(5);         // Print and display the factorial of number        // customly passed as an argument        System.out.println("Factorial of 5 is :" + ans);    }}
Output

Factorial of 5 is :120

Output explanation:

Initially, the factorial() is called from the main method with 5 passed as an argument. Since 5 is greater than or equal to 1, 5 is multiplied to the result of factorial( ) where 4 (n -1) is passed. Since, it is called from the same method, it is a recursive call. In each recursive call, the value of argument n is decreased by 1 until n reaches less than 1. When the value of n is less than or equal to 1, then there is no recursive call and at last, it returns 1.

Example 2:

## Java

 // Java Program to Find Factorial of a Number// where N>=0 is currently N=1 // Importing input output classesimport java.io.*;// Importing utility classesimport java.util.*; // Main classclass GFG {     // Method 1    // To calculate factorial    static int factorial(int n)    {         // Handling base case        // If value of n=1 or n=0 we return 1        if (n == 0 || n == 1)            return 1;         // Generic case computation math        // Otherwise we do n*(n-1)!        return n * factorial(n - 1);    }     // Method 2    // Main driver method    public static void main(String[] args)    {         // Calling Method 1 and        // storing the result into variable        int ans1 = factorial(0);        int ans2 = factorial(1);         // Print and display the factorial of 0        System.out.println("Factorial of 0 is : " + ans1);         // Similarly, Print and display the factorial of 1        System.out.println("Factorial of 1 is : " + ans2);    }}
Output
Factorial of 0 is : 1
Factorial of 1 is : 1

Output explanation:

Initially, the factorial( ) is called from the main method with 6 passed as an argument. In each recursive call, the value of argument n is decreased by 1 until n reaches less than 1. For 1! decreased argument been passed is 0! as a small recursion call to be computed. As discussed above factorial of zero is 1. Hence, the small answer returned is 1, which later is multiplied to 1 itself so do result 1 as an output. Hence, it is stated when the value of n is less than or equal to 0 then no recursion call is computed as we will encounter negative integers over which factorial is not allowed to be computed.

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