Here's a C program to check whether a given number is prime number or not with output and proper explanation. This program uses C concepts like break statement, modulus in C, IF-ELSE conditions and for loops.

What's a Prime Number?A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

# include <stdio.h> # include <conio.h> void main() { int i, n, flag = 0 ; clrscr() ; printf("Enter the Number : ") ; scanf("%d", &n) ; if(n <= 3) flag = 0 ; else { for(i = 2 ; i <= n / 2 ; i++) if(n % i == 0) { flag = 1 ; break ; } } if(flag == 1) printf("\nThe number is not prime") ; else printf("\nThe number is prime") ; getch() ; }

**Output of above program**

Enter the number : 15

The number is not prime

Enter the number : 7

The number is prime.

**Explanation of above program**

We

**have three integer variables here -**- n - is the number which we're checking to be prime.
- i - is the loop variable.
- flag - is a tracking variable. Its value is initially set to 0 and if after the completion of program its value is still 0 that means the number we entered is a prime number.

Tip: To check for a prime number we just need to check whether a number n is divisible by any number between 2 and n / 2. It is obvious because no number can be divisible by a number which is greater than its half e.g. all divisors of 18 are less than or equal to 9 i.e. half of 18. This is also true for each number. So we can reduce our for loop by half number of total iterations. Also, we can skip the checking for 1, 2 and 3 using the IF condition, setting the flag variable to 0 i.e. that number is a prime number.

In the else part we've a for loop looping for i = 2 to n / 2. Inside for loop, we check whether our number is divisible by any value of loop variable by the following expression in the IF condition -

**n % i == 0.**If this value becomes true for any value of

**i,**the if part is executed then the flag is set to 1 (indicating the number is not prime) and using

**break statement**we terminate our loop. Also if our number is a prime number, the IF condition inside the for loop will never become true and value of flag variable will be 0 i.e. indicating that the number is a prime number.

Outside the for loop and else condition, we've another IF-Else condition. This is used to check the value of flag i.e. IF the value of flag is 1 the number is not prime otherwise the number is prime.

why we put flag=0 after if

Hi Yasir!!! Flag is used to indicate whether the entered number say "n" is divisible by any number between 2 to n / 2.

If the entered number is divisible by any number between this range then value of flag becomes one and then FOR loop breaks. Outside the FOR loop, we are checking if value of FLAG is 1 then the entered number is not Prime otherwise if FLAG is 0 then the entered number is Prime.

Hope this will clear things up... :)