# Factorial of a Number in C++ using Recursion

Before going to the program first let us see what is Factorial of a Number? and what is Recursion?

Factorial of a Number:

The factorial of a Number n, denoted by n! , is the product of all positive integers less than or equal to n.

The value of 0! is 1 according to the convention for an empty product.

For example,

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Recursion:

In C programming language, if a function calls itself over and over again then that function is known as Recursive Function.

The process of function calling itself repeatedly is known as Recursion.

## Program code for Factorial of a Number using Recursion:

```/* Factorial of a number using Recursion */
#include<iostream.h>
#include<conio.h>

int fact(int);

void main()
{
int num,f;
clrscr();

cout<<"\n  Enter the number: ";
cin>>num;

f=fact(num);

cout<<"\n  The factorial of " <<num<<" is "<<f;
getch();
}

int fact(int n)
{
if(n==0||n==1)
return 1;
else
return(n * fact(n-1));
}
```

## Working:

• First the computer reads the number to find the factorial of the number from the user.
• Then using recursive function the factorial value is calculated and returns the factorial value to main function.
• Finally the factorial value of the given number is printed.

## Step by Step working of the above Program Code:

Let us assume that the number entered by the user is 5.

1. It assigns the value of n=5.
2. Then using a variable f the recursive function fact(n) is called.

2.1.   n==0 || n==1    (5==0 || 5==1)   if condition is false.

So it goes to the else part.

else

return(n * fact(n-1))      So, (return(5 * fact(4)))      // function calls itself

2.2.   n==0 || n==1    (4==0 || 4==1)   if condition is false.

So it goes to the else part.

else

return(n * fact(n-1))      So, (return(4 * fact(3)))      // function calls itself

2.3.  n==0 || n==1    (3==0 || 3==1)   if condition is false.

So it goes to the else part.

else

return(n * fact(n-1))      So, (return(3 * fact(2)))      // function calls itself

2.4.  n==0 || n==1    (2==0 || 2==1)   if condition is false.

So it goes to the else part.

else

return(n * fact(n-1))      So, (return(2 * fact(1)))      // function calls itself

2.5.  n==0 || n==1    (1==0 || 1==1)   if condition is true.

So it return the value 1 to fact(1) in step 2.4.

which further return the value to fact(2) in step 2.3.

which further return the value to fact(3) in step 2.2.

which further return the value 24 to fact(4) in step 2.1.

which further return the value 120 to in main function.

1. Finally it prints as given below

The Factorial of 5 is 120

1. Thus the program execution is completed.

## Output: 1. Bhavana shree V S says: