# Factorial of a Number in C using For 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,

4! = 4 * 3 * 2 * 1 = 24

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

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

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

//LOOP TO CALCULATE FACTORIAL OF A NUMBER
for(i=1;i<=n;i++)
{
f=f*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 for loop the value of ‘i’ is multiplied with the value of ‘f’.
• The loop continues till the value of ‘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 4.

1. It assigns the value of n=4 , i=1 , f=1
2. Then the loop continues till the condition of the for loop is true.

2.1.   i<=n    (1<=4) ,  for 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<=4) ,  for 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<=4) ,  for 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<=4) ,  for 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<=4) , for loop condition is true.

It comes out of the for loop.

1. Finally it prints as given below

The Factorial of 4 is 24

1. Thus the program execution is completed.

## Output:  