Factorial Number

FACTORIAL NUMBER

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

${\displaystyle 5!=5\times 4\times 3\times 2\times 1=120\,.}$

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

Mathematically, the formula for the factorial is as follows. If n is an integer greater than or equal to 1, then

n ! = n ( n - 1)( n - 2)( n - 3) ... (3)(2)(1)

If p = 0, then p ! = 1 by convention.

We can easily calculate a factorial from the previous one:

As a table:

n	n!
1	1	1	1
2	2 × 1	= 2 × 1!	= 2
3	3 × 2 × 1	= 3 × 2!	= 6
4	4 × 3 × 2 × 1	= 4 × 3!	= 24
5	5 × 4 × 3 × 2 × 1	= 5 × 4!	= 120
6	etc	etc

C Program for Factorial of a Number

#include <stdio.h>
int main()
{
    int n, i;
    unsigned long long factorial = 1;

    printf("Enter an integer: ");
    scanf("%d",&n);

    // show error if the user enters a negative integer
    if (n < 0)
        printf("Error! Factorial of a negative number doesn't exist.");

    else
    {
        for(i=1; i<=n; ++i)
        {
            factorial *= i;              // factorial = factorial*i;
        }
        printf("Factorial of %d = %llu", n, factorial);
    }

    return 0;
}

Output:

Enter an integer: 10
Factorial of 10 = 3628800