# Java program to find Factorial of a given number using Recursion

### Factorial:

Factorial of a non-negative integer n, is the product of all positive integers less than or equal to n. It is represented as n!.

n! = 1 * 2 * 3 * 4 * ………………… * (n-1) * n.

for example, 5! can be calculated as 5 * 4 * 3* 2 * 1 = 120.

### Recursion:

Recursion is a process in which a method calls itself continuously. A method in java that calls itself is called recursive method.

For example a factorial can be defined recursively as:

factorial(x) = x * factorial(x – 1) for x > 1

= 1 for x = 1 or x = 0

The base criteria for the function is at x = 1 or x = 0 .i.e. the function does not call itself when it reaches x = 1 or x = 0.The function calls itself whenever x is not 1 or 0 and moves closer to the base criteria as x is reduced at every recursive call.

### Algorithm:

Step 1: START.Step 2: Read number n.

Step 3: call factorial(n)

Step 4: print factorial f.

Step 5: stop.

factorial(n)

**Step 1:** If n==1 then return 1

**Step 2:** Else f=n*factorial(n-1)

**Step 3: **Return f

### Source code:

import java.util.*; class Factorial { static int factorial(int num) { if(num == 0) { return 1; } else { int fact; fact = num * factorial(num-1); return fact; } } public static void main(String args[]) { System.out.println("\n \n *** www.programmingposts.com *** \n \n"); System.out.println(">>> Java Program to find Factorial of a given number using Recursion >>> \n\n "); int fact = 1; Scanner scanner = new Scanner(System.in); System.out.println("Enter a number"); int num = scanner.nextInt(); fact = factorial(num); System.out.println("The Factorial of " + num + " is " +fact); } }

### Explanation:

The factorial of a number be found using recursion also. The base case can be taken as the factorial of the number 0 or 1, both of which are 1. The factorial of some number num is that number multiplied by the factorial of (num-1). Mathematically,

factorial ( num ) = n * factorial ( num – 1 ).

### Output:

C:\Users\santo\Desktop\new\new>javac Factorial.javaC:\Users\santo\Desktop\new\new>java Factorial

*** www.programmingposts.com ***

>>> Java Program to find Factorial of a given number using Recursion >>>

Enter a number

6

The Factorial of 6 is 720.

### Screenshot of output: