Is 253 a Prime Number?

There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties like:

• Prime numbers are positive numbers always greater than 1.
   
• 2 is the only even prime number.
   
• They have only two factors: 1 and the number itself.
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor that is 1.
   
• As 253 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 253 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. A few methods are:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. If there is a total count of only 2 divisors, then the number would be prime. If the count is more than 2, then the number is composite. Let’s check whether 253 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 253 by 2. It is not divisible by 2, so 2 is not a factor of 253.

Step 3: Divide 253 by 3. It is not divisible by 3, so 3 is not a factor of 253.

Step 4: Divide 253 by 11. It is divisible by 11, so 11 is a factor of 253.

Step 5: Continue checking divisors up to the approximate square root of 253.

Since 253 has more than 2 divisors (1, 11, 23, and 253), it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place value is 3. Since 3 is not even, 253 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 253 is 10. Since 10 is not divisible by 3, 253 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 253 is not divisible by 5.

Divisibility by 7: Perform calculations to find that 253 is not divisible by 7.

Divisibility by 11: Subtract the sum of the digits in even positions from the sum of the digits in odd positions, which is 0. Since 0 is divisible by 11, 253 is divisible by 11.

Since 253 is divisible by numbers other than 1 and itself, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1.

Through this process, we will have a list of prime numbers from 1 to 100. The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

253 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 253 as 11 × 23.

Step 2: Both 11 and 23 are prime numbers.

Hence, the prime factorization of 253 is 11 × 23.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 is a prime number.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Divisibility rules: Rules that help determine if one number is divisible by another without performing the division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 14 and 15 are co-prime.