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C Program to Check Whether a Number is Prime or not
  • Difficulty Level : Easy
  • Last Updated : 01 Mar, 2021

Given a positive integer N. The task is to write a C program to check if the number is prime or not

Definition

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are {2, 3, 5, 7, 11, ….}

The idea to solve this problem is to iterate through all the numbers starting from 2 to sqrt(N) using a for loop and for every number check if it divides N. If we find any number that divides, we return false. If we did not find any number between 2 and sqrt(N) which divides N then it means that N is prime and we will return True. 
Why did we choose sqrt(N)? 
The reason is that the smallest and greater than one factor of a number cannot be more than the sqrt of N. And we stop as soon as we find a factor. For example, if N is 49, the smallest factor is 7. For 15, smallest factor is 3.
Below is the C program to check if a number is prime: 

C




// C program to check if a
// number is prime
 
#include <math.h>
#include <stdio.h>
int main()
{
    int n, i, flag = 1;
 
    // Ask user for input
    printf("Enter a number: \n");
 
    // Store input number in a variable
    scanf("%d", &n);
 
    // Iterate from 2 to sqrt(n)
    for (i = 2; i <= sqrt(n); i++) {
 
        // If n is divisible by any number between
        // 2 and n/2, it is not prime
        if (n % i == 0) {
            flag = 0;
            break;
        }
    }
 
    if (n <= 1)
        flag = 0;
 
    if (flag == 1) {
        printf("%d is a prime number", n);
    }
    else {
        printf("%d is not a prime number", n);
    }
 
    return 0;
}

Output

Enter a number: 11
11 is a prime number

Time Complexity: O(n1/2)

Auxiliary Space: O(1)

Want to learn from the best curated videos and practice problems, check out the C Foundation Course for Basic to Advanced C.

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