# Factorial of a number using recursion

## Factorial Number

Factorial says to multiply all whole numbers from the chosen number down to 1.

The symbol is “!”

Examples:

5! =5 x 4 × 3 × 2 × 1 = 120
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Mathematically, the formula for the factorial is as follows. If n is an integer greater than or equal to 1, then

n ! = n ( n – 1)( n – 2)( n – 3) … (3)(2)(1)

The factorial values for negative integers are not defined.

### Implementation of factorial of number

First of all we want to solve this problem using recursion,recursion means Recursion is a process in which a function calls itself as a subroutine. This allows the function to be repeated several times, since it calls itself during its execution.

initialize n and f variable and fact is a function the function is call itself by repetition . if n equal 0 then return 1 else return (n*fact(n-1)).

#### Code of factorial of number using recursion

`  #include<stdio.h>  int fact(int);  void main(){  int n,f;  printf("enter number for finding factorial\n");  scanf("%d",&n);  f=fact(n);  printf("factorial is%d",f);}  int fact(int n){  if(n==0)     return 1;  else    return(n*fact(n-1));}`

#### Output

`enter number for finding factorial4factorial is 24`