# Factorial of a Number in C using while Loop

Before going to the program first let us understand what is a Factorial of a Number?

Factorial of a Number:

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

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

For example,

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

## Program code for Factorial of a Number in C:

```#include<stdio.h>
#include<conio.h>
void main()
{
int n,i=1,f=1;
clrscr();

printf("\n Enter The Number:");
scanf("%d",&n);

//LOOP TO CALCULATE FACTORIAL OF A NUMBER
while(i<=n)
{
f=f*i;
i++;
}

printf("\n The Factorial of %d is %d",n,f);
getch();
}
```

## Working:

• First the computer reads the number to find the factorial of the number from the user.
• Then using while loop the value of ‘i’ is multiplied with the value of ‘f’.
• The loop continues till the value of ‘i’ is less than or equal to ‘n’.
• Finally the factorial value of the given number is printed.

## Step by Step working of the above Program Code:

Let us assume that the number entered by the user is 6.

1. It assigns the value of n=6 , i=1 , f=1
2. Then the loop continues till the condition of the while loop is true.

2.1.   i<=n    (1<=6) ,  while loop condition is true.

f=f*i    (f=1*1)    So  f=1

i++      (i=i+1)    So  i=2

2.2.   i<=n    (2<=6) ,  while loop condition is true.

f=f*i    (f=1*2)    So  f=2

i++      (i=i+1)    So  i=3

2.3.   i<=n    (3<=6) ,  while loop condition is true.

f=f*i    (f=2*3)    So  f=6

i++      (i=i+1)    So  i=4

2.4.   i<=n    (4<=6) ,  while loop condition is true.

f=f*i    (f=6*4)    So  f=24

i++       (i=i+1)    So  i=5

2.5.   i<=n    (5<=6) ,  while loop condition is true.

f=f*i    (f=24*5)    So  f=120

i++       (i=i+1)    So  i=6

2.6.   i<=n    (6<=6) ,  while loop condition is true.

f=f*i    (f=120*6)    So  f=720

i++       (i=i+1)    So  i=7

2.7.   i<=n    (7<=6) ,  while loop condition is false.

It comes out of the while loop.

1. Finally it prints as given below

The Factorial of 6 is 720

1. Thus the program execution is completed.

## Output:  1. fetene tadege says: