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.

Related: Factorial of a Number in C++ without using 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));
}

Related: Factorial of a Number in C using Recursion

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 2 to fact(2) in step 2.3.

which further return the value 6 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 f in main function.

3. Finally it prints as given below

The Factorial of 5 is 120

4. Thus the program execution is completed.

Output:

TO DOWNLOAD THE PROGRAM CODE :CLICK HERE