Factorial is used in many areas of mathematics but mainly used in permutation and combination. Factorial is the product of the all positive number from 1 to n (user entered number). In simple words, we can say that factorial of n would be 1*2*3*…..*n.

Note: There is no factorial exist for the negative number and the value of !0 is 1.

Factorial of positive number would be:

!n  = n * !(n-1)

For example,

!5 =  5*4*3*2*1*!0  =  120.

Some factorials of numbers

Here I am describing the few methods to calculate the factorial of a positive number in C. I hope you are familiar with while and for loop in C.

1) Factorial of a number in C using the for loop

The below program takes a positive integer number from the user and computes its factorial using the for loop.

#include <stdio.h>


int main(int argc, char *argv[])
{

    unsigned int iLoop,iFactorial = 1;
    int iNumber=0;

    printf("Enter a number: ");
    scanf("%d",&iNumber);

    if(iNumber < 0 )
    {
        printf("factorial of negative number dose not exist\n\n\n");
    }
    else
    {
        for(iLoop=1; iLoop<=iNumber; iLoop++)
        {
            iFactorial*= iLoop;
        }

        printf("\n\nFactorial of %d is: %u\n\n\n\n",iNumber,iFactorial);
    }

    return 0;
}

OutPut

When the user Enters the negative number.

When the user enters the positive number.

2.) Factorial of a number using the recursive method.

A function is called recursive, if it is called by itself. You can see this article, Recursion in C. Before writing the code I want to show here a flow diagram which to describe the flow of the code.

#include <stdio.h>

//Calculate factorial in C
unsigned long fact(unsigned long int n)
{
    if (n == 0)
    {
        return 1;
    }
    else
    {
        return(n * fact(n - 1));
    }
}


//Driving function
int main(int argc, char *argv[])
{
    unsigned long  n = 0;
    unsigned result = 0;

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

    //check negative number
    if (n < 0)
    {
        printf("\nFactorial of a negative number dose not exist \n");
    }
    else
    {
        result = fact(n);
        printf("\nThe Factorial of %d is : %d.\n", n, result);
    }

    return 0;
}

Output:

Working of the above code,

Here n = 3

fact(3) = 3 * fact(2)
fact(2) = 2* fact(1)
fact(1) = 1 *fact(0);

When n=0, condition becomes true and recursion stops and control returns to factorial(1). Now reverse process occurs and function will return a value to the previous function calls.

Note: There should be a termination point in a recursive function.

So the final result will be:

fact(3) = 3*2*1 = 6

You can also see the below articles,

• Recursion in C and its advantages and disadvantages.

3.) Factorial of a number in C using the while loop

#include <stdio.h>


int main(int argc, char *argv[])
{
    unsigned int iLoop = 1,iFactorial = 1;
    int iNumber = 0;

    printf("\n\nEnter a number: ");
    scanf("%d",&iNumber);

    if(iNumber < 0 )
    {
        printf("factorial of negative number dose not exist\n\n\n");
    }
    else
    {
        while(iLoop <= iNumber)
        {
            iFactorial*= iLoop; // product from 1 to n
            iLoop++; // Increment the value
        }

        printf("\n\nFactorial of %d is: %u\n\n\n\n",iNumber,iFactorial);
    }

    return 0;
}

4.) Calculate the factorial using the look-up table

If you need the factorial of the small number then the look-up table is the best option because it is fast as compared to iteration and recursion method.

In below program, I am creating a look-up table which contains the factorial of-of 0 to 10;

#include <stdio.h>

//Function returns the factorial
int iReturnFactorial(int index);

int main(int argc, char *argv[])
{

    long int iFactorial =1;
    int iNumber = 0;

    printf("Enter a positive integer number: ");
    scanf("%d", &iNumber);
    if (iNumber < 0)
    {
        printf("\nFactorial of a negative number dose not exist \n");
    }
    else
    {
        iFactorial = iReturnFactorial(iNumber);
        printf("\nThe Factorial of %d is : %lu\n", iNumber, iFactorial);
    }
    return 0;
}

int iReturnFactorial(int index)
{
    //Look up table
    const int acFactValue [11]= {1,1,2,6,24,120,720,5040,40320,362880,3628800};

    return acFactValue[index];
}

5.) Calculate the factorial using a function

#include <stdio.h>

//Function calculate factorial
int iCalculateFactorial(int);

int main(int argc, char *argv[])
{
    int iFactorial =1,iNumber=0;

    printf("Enter a positive integer number: ");
    scanf("%d", &iNumber);
    if (iNumber < 0)
    {
        printf("\nFactorial of a negative number dose not exist \n");
    }
    else
    {
        iFactorial = iCalculateFactorial(iNumber);
        printf("\nThe Factorial of %d is : %d \n", iNumber, iFactorial);
    }

    return 0;
}

int iCalculateFactorial(int iNumber)
{
    int iLoop, iFactorial = 1;

    for(iLoop=1; iLoop<=iNumber; iLoop++)
    {
        iFactorial*= iLoop;
    }

    return iFactorial;
}

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