# Prime Number

## Checking if a Number is Prime

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number has exactly two distinct factors: 1 and the number itself.

To determine whether a number is prime, we can use a method that involves checking divisibility by numbers starting from 2 up to the square root of the given number. If the number is divisible by any of these, it is not prime. If no divisors are found, the number is prime.

## Examples

Let’s examine some examples to see how this method works in practice.

### 1. Check if 13 is a prime number.

#### Answer

First, we identify the given number:

**Given:**

**n**= 13

Next, we calculate the square root of 13, which is approximately 3.6. We then check if 13 is divisible by any number from 2 up to 3 (the integer part of the square root):

**Steps:**

- Check divisibility by 2: 13 % 2 ≠ 0
- Check divisibility by 3: 13 % 3 ≠ 0

Since 13 is not divisible by any of these numbers, it has no divisors other than 1 and 13 itself.

**Result:**

∴ 13 is a prime number.

### 2. Check if 10 is a prime number.

#### Answer

We start by identifying the number:

**Given:**

**n**= 10

The square root of 10 is approximately 3.2. We check if 10 is divisible by any number from 2 up to 3:

**Steps:**

- Check divisibility by 2: 10 % 2 = 0

Since 10 is divisible by 2, it has a divisor other than 1 and itself.

**Result:**

∴ 10 is not a prime number.

### 3. Determine if 17 is a prime number.

#### Answer

We begin by identifying the number:

**Given:**

**n**= 17

The square root of 17 is approximately 4.1. We check if 17 is divisible by any number from 2 up to 4:

**Steps:**

- Check divisibility by 2: 17 % 2 ≠ 0
- Check divisibility by 3: 17 % 3 ≠ 0
- Check divisibility by 4: 17 % 4 ≠ 0

Since 17 is not divisible by any of these numbers, it has no divisors other than 1 and 17 itself.

**Result:**

∴ 17 is a prime number.

### 4. Verify if 25 is a prime number.

#### Answer

We start by identifying the number:

**Given:**

**n**= 25

The square root of 25 is exactly 5. We check if 25 is divisible by any number from 2 up to 5:

**Steps:**

- Check divisibility by 2: 25 % 2 ≠ 0
- Check divisibility by 3: 25 % 3 ≠ 0
- Check divisibility by 4: 25 % 4 ≠ 0
- Check divisibility by 5: 25 % 5 = 0

Since 25 is divisible by 5, it has a divisor other than 1 and itself.

**Result:**

∴ 25 is not a prime number.