Program Factorial by While Loop Logic

Q: Write a program in C++ to input a number and display its factorial. Use while Loop.

Easyway How to Write a program in C++ to input a number and display its factorial

Program factorial : How to understand mathematical  Logic behind factorial?

We know that factorial of a number is equal to the product of all numbers from one to the given number. For example
Factorial of  3 = 1 x 2 x 3   hence 6
Factorial of  4 = 1 x 2 x 3 x 4 , hence 24
Similarly Factorial of  N = 1 x 2 x 3 .......... x n
If  N = 5 then
Factorial = 1 x 2 x 3 x 4 x 5 , hence 125
Which Statements we Need For Factorial Program?
1. We need cout<< for displaying messages and results to the user.
2. We need cin>> for inputting a number.
3. We need assignment statement, for example fact = 1;
4. We need a while loop statement to multiply all numbers from 1 to N.
And above all we need some variable declarations as well.

Coding : Find Factorial of a Number by while Loop

/*
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// Program To Input a Number and Find
// its Factorial by while Loop
#include<iostream>
#include<conio.h>


 int main()                  
 {
   int num;
   clrscr();
   cout<<"Enter a Number to Display\nits Factorial=";
   cin>>num;

   long i=1, fact=1;
   while(i<=num)
   {
   fact = fact * i;
   i++;
   }
   cout<<"Factorial of "<<num<<" = "<<fact<<endl;
   getch();
   return 0;  
 }

 A Sample Run on Paper of Program Factorial

1.  Let we input 3.
2. Now num = 3, we also initialize i and fact variables to 1.So that now i = 1 and fact =1
3. Condition of While loop is tested (i<=num) putting the values 1<=3 which is true.
4. So while loop starts

     First Iteration

      fact = fact * i
      before execution
      1   =  1    *   1
      fact =1 and i = 1
      after execution
      fact =1  and i =1
     The value of i is incremented by 1 so i=2

     

Second Iteration

Since i<=num that is 2<=3 is true so loop takes second iteration    
      fact = fact * i
      before execution
      1   =  1    *   2
      fact =1 and i = 2
      after execution
     fact =2  and i =2
     Note: First of all, Right hand side expression (1 * 2) is evaluated and the result is assigned to the variable fact on left hand side of  =.
The value of i is incremented by 1 so i=3

Third Iteration

Since i<=num that is 3<=3 is true so loop takes third iteration    
      fact = fact * i
      before execution
      2   =  2    *   3
      fact =2 and i = 3
      after execution
      fact =6  and i =3
     The value of i is incremented by 1 so i=4

 Since i<=num that is 4<=3 is false so loop ends now.

The control goes to next statement which is
  cout<<"Factorial of "<<num<<" = "<<fact<<endl;
So it will print Factorial of 3 = 6