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,

5 ! = 5 * 4 * 3 * 2 * 1 = 120

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

```#include<iostream.h>
#include<conio.h> void main()
{ int n,f=1,i=1; clrscr(); cout<<"n Enter The Number:"; cin>>n; //LOOP TO CALCULATE THE FACTORIAL OF A NUMBER do { f=f*i; i++; }while(i<=n); cout<<"n The Factorial of "<<n<<" is "<<f; getch();
}
```

Related: Factorial of a Number in C using do-while Loop

## Working:

• First the computer reads the number to find the factorial of the number from the user.
• Then using do-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 5.

1. It assigns the value of n=5 , i=1 , f=1
2. Then the loop continues till the condition of the do-while loop is true.

2.1.   do

f=f*i    (f=1*1)    So  f=1

i++      (i=i+1)    So  i=2

i<=n    (2<=5) , do-while loop condition is true.

2.2.   do

f=f*i    (f=1*2)    So  f=2

i++      (i=i+1)    So  i=3

i<=n    (3<=5) , do-while loop condition is true.

2.3.   do

f=f*i    (f=2*3)    So  f=6

i++      (i=i+1)    So  i=4

i<=n    (4<=5) , do-while loop condition is true.

2.4.   do

f=f*i    (f=6*4)    So  f=24

i++       (i=i+1)    So  i=5

i<=n    (5<=5) , do-while loop condition is true.

2.5.   do

f=f*i    (f=24*5)    So  f=120

i++       (i=i+1)    So  i=6

i<=n    (6<=5) , do-while loop condition is false.

2.6.   It comes out of the do-while loop.

1. Finally it prints as given below

The Factorial of 5 is 120

1. Thus the program execution is completed.