# Factorial Program in C++

Factorial Program in C++ | In mathematics, the factorial of a positive integer n, denoted by n! Factorial is the product of all positive integers less than or equal to n. For example:- The factorial of 4= 4! = 4*3*2*1 or 1*2*3*4 = 24

Factorial (n) = 1 * 2 * … * (n-1) * n
Or,
n * (n-1) * … * 2 * 1

The factorial of a negative number doesn’t exist. The value of 0! is 1, according to the convention for an empty product.

Procedure to find the factorial of a number in C++,

1) Take a number
2) Declare a temporary variable fact and initialize it with 1. Since factorial will be a large number so better to take a long data type. long fact = 1;
3) Take an iterator variable i, starting from 1
4) Multiply fact variable and iterator variable. Store the result into the fact variable. fact = fact * i;
5) Increase the iterator variable by 1.
6) Repeat 4 and 5 steps until the iterator variable is less than the input number.

## C++ Program to Find Factorial of a Number

Using this we can write a program to find the factorial of a number in C++,

``````// C++ program to find factorial
// of a number using For Loop
#include<iostream>
using namespace std;
int main()
{
// declare variables
int num;
long factorial=1;

// take input
cout << "Enter a positive integer : ";
cin >> num;

// calculate factorial
for (int i=1; i<=num; i++)
{
factorial = factorial * i;
}

// display result
cout << "Factorial = " << factorial << endl;

return 0;
}``````

Output for the different test-cases:-

Enter a positive integer: 3
Factorial = 6

Enter a positive integer: 5
Factorial = 120

Enter a positive integer: 10
Factorial = 3628800

Enter a positive integer: 20
Factorial = 2432902008176640000

In this program, we have used a for loop and increment operator, but we can also use decrement operator. Below is the code using for loop and decrement operators,

``````// calculate factorial
for (int i=num; i > 0; i--)
{
factorial = factorial * i;
}``````

We can also use while loop in place of for loop. And in the case of while loop again we can use either increment operator or decrement operator.

``````// C++ program to find factorial of a number using while Loop
#include<iostream>
using namespace std;
int main()
{
// declare variables
int num;
long factorial=1;

// take input
cout << "Enter a positive integer : ";
cin >> num;

// calculate factorial using while loop
while (num != 0)
{
factorial = factorial * num;
num--;
}

// display result
cout << "Factorial = " << factorial << endl;

return 0;
}``````

## Using Function

Based on the above programs we can develop a function to calculate factorial value. The function will take numbers as arguments and return the factorial value to the called function. The function will be written as,

``````// function to calculate Factorial value
long findFactorial(int number)
{
// declare variable
long fact = 1;

// calculate factorial value
for(int i=number; i>1; i--) {
fact = fact * i;
}

// return result
return fact;
}``````

## Factorial Program in C++ using Function

Using the above factorial function to calculate the factorial value of a number, we can write a factorial program in C++ using Function. It can be written as below,

``````// C++ program to find factorial
// of a number using while Loop
#include<iostream>
using namespace std;
long findFactorial(int);
int main()
{
// declare variables
int num;

// take input
cout << "Enter a positive integer : ";
cin >> num;

// display result
cout << "Factorial = " << findFactorial(num) << endl;

return 0;
}

// function to calculate Factorial value
long findFactorial(int number)
{
// declare variable
long fact = 1;
// calculate factorial value
for(int i=number; i>1; i--) {
fact = fact * i;
}
// return result
return fact;
}``````

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