# C Program to Check Whether a Number is Prime or not

Given a positive integer . 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 program to check if a ` `// number is prime ` ` `  `#include ` ` `  `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 n/2 ` `    ``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` `(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
```

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