C Program: Factorial of a Number

The factorial of a given positive integer $n$ is defined as the product of all whole numbers from 1 to $n$.

It is denoted by $n!$

c program factorial

$n! = n\times(n-1)\times ... \times1$

We calculate factorials only of positive integers, hence we specify the input number n as of type unsigned short int. The counter i will also always be positive, hence it is also assigned to type unsigned short int. The computed factorial factorial again is always going to be a positive, hence, we define it to be of type unsigned long int.

Also, note that $0! = 1$.

Below we write a C program which computes the factorial of a given number $n$. 

				
				#include <stdio.h>

				int main() {
					unsigned short int i, n;
					unsigned long int factorial = 1;

					printf("Enter a positive integer: ");
					scanf("%hu", &n);

					for(i = 1; i <=n; i++) {
						factorial = factorial * i;
					}

					printf("Factorial of %hu is %lu \n", n, factorial);

					return 0;
				}

We run the program to compute $5!$ and get the output as shown below: 

				
					$ ./a.out
					Enter a positive integer: 5
c program factorial output

There is a powerful online computing engine called Wolfram Alpha which you can use for getting accurate factorials of big numbers.

Below we compute the factorial of 12.

wolfram alpha factorial

We can also define a recursive function and call it to compute the required factorial as shown in the program below. 

				
				#include <stdio.h>

				unsigned long factorial(unsigned short int);

				int main() {
					unsigned short int n;

					printf("Enter a positive integer: ");
					scanf("%hu", &n);

					printf("Factorial of %hu is %lu", n, factorial(n));

					return 0;
				}

				unsigned long factorial(unsigned short n) {
					unsigned long f;
					
					if(n == 0 || n == 1)
						return 1;
					else 
						f = n * factorial(n-1);

					return f;
				}