## Check Given Number Is Prime Or Not Using While Loop in C

In this tutorial, you will learn how to write a C program to check whether a given number is a prime number or not using a while loop conditional statement. Here, we will go through examples, algorithms, logic, and program explanation for a better understanding of this problem in C programming language.

## Problem Statement

You have to Write a C program that takes a number as input from the user. After taking the integer input our program should check whether it is a prime number or not using a while loop. The program provides a solution to determine the primality of a given number using a while loop in the C programming language.

To understand what we have to achieve, you can see the below example.

Example

``````Input:
Enter a number: 17

Output:
17 is a prime number.``````

In the above example, you can see that the user input is 17. And we know that by the definition of prime number, 17 is a Prime number because it is divided by 1 and 17 only.

## Algorithm

1. Start the program.
2. Declare the variable `num` to store the input number, `isPrime` to store the prime status, and `i` as a counter.
3. Read the value of `num` from the user.
4. Initialize `isPrime` to 1 (true).
5. Initialize `i` to 2.
6. Enter the while loop with the condition `i <= sqrt(num)`.
• Check if `num` is divisible by `i` without a remainder.
• If true, set `isPrime` to 0 (false) and break out of the loop.
• If false, continue to the next iteration.
• Increment `i` by 1.
7. Exit the while loop.
8. Check the value of `isPrime`.
• If `isPrime` is 1, print that `num` is a prime number.
• If `isPrime` is 0, print that `num` is not a prime number.
9. End the program.

## Logic used to solve this Problem

• Declare a variable to hold the input number.
• Prompt the user to enter a number.
• Read and store the entered number in the variable.
• Check if the number is less than 2. If true, it is not a prime number.
• Check if the number is exactly 2. If true, it is a prime number.
• Initialize a divisor variable to 2.
• Use a while loop to iterate while the divisor is less than the square root of the number.
• Inside the loop, check if the number is divisible evenly by the divisor. If true, it is not a prime number.
• Increment the divisor by 1.
• If the loop completes without finding any divisors, the number is a prime number.
• Print the result indicating whether the number is prime or not.
• Finish the program.
• Use a while loop to iterate while the divisor is less than the square root of the number.

## C Program to Check whether a given number is Prime or not

``````#include <stdio.h>
#include <math.h>
int main() {
int num, isPrime = 1, i = 2;
printf("Enter a number: ");
scanf("%d", &num);
while (i <= sqrt(num)) {
if (num % i == 0) {
isPrime = 0;
break;
}
i++;
}
if (isPrime == 1) {
printf("%d is a prime number.\n", num);
} else {
printf("%d is not a prime number.\n", num);
}
return 0;
}``````

Output 1

``````Enter a number: 54
54 is not a prime number``````

Output 2

``````Enter a number: 5
5 is a prime number``````

### Program Explanation

• The program takes input for the number to be checked by the user.
• It initializes a variable `isPrime` to 1, which represents the initial assumption that the number is prime.
• It initializes a variable `divisor` to 2, which will be used to check divisibility.
• The program enters a while loop with the condition `divisor <= number/2` to iterate through possible divisors.
• Inside the while loop, it checks if the number is divisible by the current value of `divisor`.
• If the number is divisible, it sets the value of `isPrime` to 0, indicating that it is not a prime number.
• It then increments the value of `divisor` by 1 to move on to the next possible divisor.
• The loop continues until `divisor` exceeds half of the given number.
• After the while loop, it checks the value of `isPrime`.
• If `isPrime` is 1, it prints that the given number is prime.
• Otherwise, it prints that the given number is not prime.
• The program ends.

## Conclusion

The C program successfully checks whether a given number is prime or not using a while loop. By iterating through the numbers from 2 to the square root of the number and checking for any divisors, it determines the prime status and displays the result on the screen.