# Is 253 prime?

#### Understand the Problem

The question is asking whether the number 253 is a prime number, which means it can only be divided by 1 and itself without resulting in a fraction. We will check for divisibility by prime numbers up to the square root of 253.

No, 253 is not a prime number.

The number 253 is not a prime number.

#### Steps to Solve

1. Determine the square root of 253

The first step is to find the square root of 253 to know the range of prime numbers we need to check.

$$\sqrt{253} \approx 15.9$$

So we need to check for prime numbers up to 15.

1. List prime numbers up to 15

The prime numbers less than or equal to 15 are 2, 3, 5, 7, 11, and 13.

1. Check divisibility by 2

253 is odd, so it is not divisible by 2.

1. Check divisibility by 3

Sum the digits of 253:

$$2 + 5 + 3 = 10$$

Since 10 is not divisible by 3, 253 is not divisible by 3.

1. Check divisibility by 5

Since 253 does not end in 0 or 5, it is not divisible by 5.

1. Check divisibility by 7

Divide 253 by 7:

$$253 \div 7 = 36.142857...$$

Since the result is not an integer, 253 is not divisible by 7.

1. Check divisibility by 11

Alternate sum of the digits of 253:

$$2 - 5 + 3 = 0$$

Since 0 is divisible by 11, 253 is divisible by 11.

Therefore, since 253 is divisible by 11, it is not a prime number.

The number 253 is not a prime number.