# Factorial program in C Factorial program in C using a for loop, using recursion and by creating a function. Factorial is represented by '!', so five factorial is written as (5!), n factorial as (n!). Also, n! = n*(n-1)*(n-2)*(n-3)...3.2.1 and zero factorial is defined as one, i.e., 0! = 1.

## Factorial in C using a for loop

#include <stdio.h>

int main()
{
int c, n, f = 1;

printf("Enter a number to calculate its factorial\n");
scanf("%d", &n);

for (c = 1; c <= n; c++)
f = f * c;

printf("Factorial of %d = %d\n", n, f);

return 0;
}

Output of C factorial program: As n! grows at a faster rate than exponential function 2n, overflow occurs even for two-digit numbers if we use built-in data type. To calculate factorials of such numbers, we need to use data structures such as array or strings.

## Factorial program in C using recursion

#include<stdio.h>

long factorial(int);

int main()
{
int n;
long f;

printf("Enter an integer to find its factorial\n");
scanf("%d", &n);

if (n < 0)
printf("Factorial of negative integers isn't defined.\n");
else
{
f = factorial(n);
printf("%d! = %ld\n", n, f);
}

return 0;
}

long factorial(int n)
{
if (n == 0) // Base case
return 1;
else
return (n*factorial(n-1));
}

In recursion, a function calls itself. In the above program, the factorial function is calling itself. To solve a problem using recursion, you must first express its solution in recursive form.

## C program to find factorial of a number

#include <stdio.h>

long factorial(int);

int main()
{
int n;

printf("Enter a number to calculate its factorial\n");
scanf("%d", &n);

printf("%d! = %ld\n", n, factorial(n));

return 0;
}

long factorial(int n)
{
int c;
long r = 1;

for (c = 1; c <= n; c++)
r = r * c;

return r;
}

To calculate the number of permutations, combinations, and to compute the probability, we use factorials.