# Factorial of a number using Recursion

Factorial of a number is defined as the product of natural numbers starting from 1 to the number that we want to find factorial for. Mathematically, it is defined as follows.

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

For example, 5!= 1*2*3*4*5=120

Algorithm or Mathematical Generating Function can be written as follows.

``````f(n)= 1                    if n=0;
f(n)= n*f(n-1)             if n>0;``````

It is very easy to transform above algorithm or generating function into program that uses Recursion. Below one is the implementation in Java.

## Factorial of a given number using Recursion in Java

Here is the implementation for  Factorial of a number using recursion

```package com.jminded.recursion;

public class FactorialUsingRecursion {

/**
* <p>Factorial using Recursion</p>
* @author Umashankar
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
System.out.println(factorial(3));
System.out.println(factorial(0));
System.out.println(factorial(-7));

}
/**
* Recursion :: A method calls to it self
* <p>Mathematical defintion of factorial</p>
*
* 		f(n)= 1          if  n=0;
* 		f(n)= n*f(n-1)   if  n>0;
*
* @param n
*/
public static int factorial(int n){
//base case
if(n==0)
return 1;
//recursive case
else if(n>0)
return n*factorial(n-1);
//for negative numbers and non integers factorial is undefined.
else
return -1;
}

}```