# Prime number or Not in C using For Loop

Before going to the program for Prime Number or Not first let us understand what is a Prime Number?

Prime Number:

A Prime Number is a number greater than 1 and which is only divisible by 1 and the number itself.

For example,

11 is a Prime Number, because 11 is not divisible by any number other than 1 and 11.

To find whether a Number is Prime Number or Not it is enough to check whether ‘n’ is divisible by any number between 2 and √n. If it is divisible then ‘n’ is not a Prime Number otherwise it is a Prime Number.

## Program code for Prime Number or Not in C:

```/* Prime Number or Not */
#include<stdio.h>
#include<conio.h>
#include<math.h>

void main()
{
int n, i, flag=0;
clrscr();

printf("\n\n  Enter a positive integer value: ");
scanf("%d",&n);

/* Loop to check whether 'n' is divisible by any number between 2 and sqrt(n) */
for(i=2;i<=sqrt(n);i++)
{
if(n%i==0)
{
flag=1;
break;
}
}

/* if else condition to print Prime Number or Not */
if (flag==0)
{
printf("\n  %d is a prime number.",n);
}
else
{
printf("\n  %d is not a prime number.",n);
}
getch();
}
```

## Working:

• First the computer reads the positive integer value from the user.
• Then using for loop it checks whether ‘n’ is divisible by any number between 2 and √n.
• Finally if else condition is used to print the number is prime number or not .

## Step by Step working of the above Program Code:

For Prime Number:

1. Let us assume that a user enters the positive integer value as 13.
2. It assigns the value of flag=0, n=13.
3. It assigns the value of i=2 and the loop continues till the condition of the for loop is true.

3.1.   i<=sqrt(n)    (2<=√13)    for loop condition is true

n%i==0    (13%2==0)    if condition is false

i++            (i=i+1)     So  i=3

3.2.   i<=sqrt(n)    (3<=√13)    for loop condition is true

n%i==0    (13%3==0)    if condition is false

i++            (i=i+1)     So  i=4

3.3.   i<=sqrt(n)    (4<=√13)    for loop condition is false

It comes out of the for loop.

1. flag==0    (0==0)    if condition is true

So it prints 13 is a prime number.

1. Thus program execution is completed.

For Not a Prime Number:

1. Let us assume that a user enters the positive integer value as 9.
2. It assigns the value of flag=0, n=9.
3. It assigns the value of i=2 and the loop continues till the condition of the for loop is true.

3.1.   i<=sqrt(n)    (2<=√9)    for loop condition is true

n%i==0    (9%2==0)    if condition is false

i++            (i=i+1)     So  i=3

3.2.   i<=sqrt(n)    (3<=√9)    for loop condition is true

n%i==0    (9%3==0)    if condition is true

It assigns flag=1

breaks the loop and comes out of the for loop

1. flag==0    (1==0)    if condition is false

So it goes to else part and prints 9 is not a prime number.

1. Thus program execution is completed.

## Output:  