## 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.

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