### for loop Programs In C:

Q1. Write a C program to find factorial of a number by accepting the number from user.
Ans.
#include<stdio.h>
#include<conio.h>
void main()
{
int n, i, fact=1;
clrscr();
printf("\n enter the number for finding factorial");
scanf("%d",&n);
for(i=1;i<=n;i++)
{
fact=fact*i;
}
printf("\n the factorial of %d is %d",n,fact);
getch();
}

### Output:

enter the number for finding factorial
5
the factorial of 5 is 120

### Explanation of the above Code:

First of all
What is factorial?
Ans.
The symbol of factorial is !
here are example which will give you idea what is factorial
ex.
5!=5*4*3*2*1
3!=3*2*1
Now you have the idea what is factorial.
• In the above code we have declared 3 variables of datatype integer i for the loop, fact=1 for calculating the factorial, n for input.
• When the loop gets started with i=1 it checks the condition first i.e whether i is less than n (1<=5) which in this case is true since the initial value of i is 1 and the value of n is 5.
• After entering the loop we have the code fact=fact*i ; it  happens like this fact=1*1 since the initial values of both fact and i is 1. Now the value of 1 is assigned to fact.
• Now increment takes place and the value of i becomes 2. As the condition is true it enters the loop again and executes the code like this fact=1*2; now the value of fact becomes 2.
• Now increment takes place and the value of i becomes 3. As the condition is true it enters the loop again and executes the code like this fact=2*3; now the value of fact becomes 6.
• This goes on till the value of i becomes equal to n that is 5 in this case.
• After reaching 5 the value of fact becomes equal to 5 factorial and the value is finally printed.

### Same Program using while loop:

#include<stdio.h>
#include<conio.h>
void main()
{
int n, i=1, fact=1;
clrscr();
printf("\n enter the number for finding factorial");
scanf("%d",&n);
while(i<=n)
{
fact=fact*i;
i++;
}
printf("\n the factorial of %d is %d",n,fact);
getch();
}

### Output:

enter the number
5
the number is prime number

### Explanation of the above Code:

First of all
What is prime number?
Ans.
A number which is divisible by 1 and only itself is called a prime number. Also a number which is divisible has remainder 0.
So in all a number which is divisible twice that is it has remainder 0 twice only is a prime number.
• In the above code we have declared 4 variables of datatype integer n for input, i for the loop, r for calculating remainder and c for counting how many times the remainder is 0 i.e how many times the number is divisible.
• In the for loop we one by one check, how many times the number was divisible  by dividing the number n by the numbers from 1 to n and increasing the value of c if it is divisible.
• So the first value which enters the loop is i=1 then the remainder is calculated by r i.e r=5%1 which is 0 since 5 is divisible by 1 and now the value of loop increases from 0 to 1.
• Now the value of i becomes 2 again the remainder is calculated  by r=5%2 which is 1 in this case so the value of c remains the same.
• Similarly the value of c remains same for 3 and 4 because their remainders are 2 and 1 respectively.
• Now 5 is divisible by 5 and the remainder becomes 0 so the value of c increases from 1 to 2.
• After coming out of for loop we compare the values of c. If the value of C is equal to 2 i.e the number is divisible twice and its a prime number.
• Else its not a prime number

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