Java Program to Find Factorial of a Number Recursively

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 classes
import java.io.*;
// importing utility classes
import java.util.*;

// Main class
class 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

Time Complexity: O(n),The time complexity of the above code is O(n) as the recursive function is called n times. 
Space Complexity: O(n),The space complexity is also O(n) as the recursive stack of size n is used.

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 classes
import java.io.*;
// Importing utility classes
import java.util.*;

// Main class
class 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.