Introduction

In this program, you will learn to calculate the factorial of a number entered by the user using the process of recursion.

The factorial of a positive integer ‘x’ is 1*2*3*4*……..*x.

For example, Factorial of 5 is (! is the symbol for factorial):

5! =5*4*3*2*1=120

Similarly, Factorial of 7 is

7! =7*6*5*4*3*2*1=5040

Factorial of negative numbers doesn’t exist.

Factorial of 0 and 1 is 1.

What is the use of this program?

It is easy to calculate the factorial up to certain values but it is difficult to calculate factorial like 100! , 500! etc. A small code written in C++ will make this task quite easy.

To understand this example, you should know about the following C++ programming topics:

1. Data types

2. Operators

3. Recursion

4. User-defined functions

Recursion is the process in which a function calls itself.

Program

#include<iostream>
using namespace std;
int factorial (int x)
{
if(x==0)
{
return 1;
}
else
{
return x*factorial(x-1); // recursive call
}


}
int main()
{
int n;
cout<<"Enter a positive integer: ";
cin>>n;


int fact=1; // fact to store the factorial
if(n>=0) // if n is positive integer
{
fact=factorial(n);
cout<<"Factorial of "<<n<<" is "<<fact;
}
else // if n is negative integer
{
cout<<"factorial doesn't exist";
}


return 0;
}

Output

Explanation

In the above program, we have to calculate the factorial of ‘n’.

The user is asked to enter the value of ‘n’.

If ‘n’ is a positive number only, then we will proceed with the ‘factorial’ function else, ‘n’ is a negative number, and the statement “factorial doesn’t exist” gets printed.

factorial is a user-defined function declared with ‘int’ type, and ‘x’ is passed as an argument in it.

Now, we have only two options.

Either ‘x’ is 0 for that factorial will be 1

Or ‘x’ is greater than 0, and for that recursion, the process will take place.

return x*factorial(x-1);

factorial function calls itself with decreasing values of ‘x’ each time.