Is 252 a prime number?

The number 252 has 10 factors that divide it completely without leaving any remainder. Thus, 252 is a non-prime number. The factors of 252 include 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

For a number to be prime, it must have exactly two factors: 1 and the number itself. Since 252 has more than two factors, it is classified as a composite number.

Below are several methods used to determine whether a number is prime or composite.

The different methods we can use to check if a number is a prime number are explained below:
 

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization

In this method, we count how many divisors the number has. If the count is more than 2, it is composite.

The counting divisors method for 252 would simply be:

Divisors of 252 = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Number of divisors = 18

Since the number has more than 2 divisors, 252 is a composite number.

In the divisibility method, we divide the number by smaller prime numbers. If it is divisible by any prime number other than itself and 1, it is composite.

The divisors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

Since 252 has many divisors other than 1 and itself, it is not a prime number.
 

The prime number chart is a list of prime numbers starting from 2 to infinity.

The list of prime numbers under 300 includes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251.

Since 252 is not present in the list, it is not a prime number.
 

This method is only used for non-prime or composite numbers. Since 252 is a composite number, its prime factorization is:

Factors of 252 = 2²×3²×7
 

• Prime Number: A number greater than 1 that has exactly two factors: 1 and itself. Examples include 2, 3, 5, and 7.

• Composite Number: A natural number greater than 1 that has more than two factors. For example, 252 is a composite number because it has multiple divisors such as 1, 2, 3, 4, etc.

• Divisibility: A term used to describe whether one number can be divided by another number without leaving a remainder. For example, 252 is divisible by 2, 3, 7, etc.

• Prime Factorization: The process of breaking down a number into its prime factors. The prime factorization of 252 is 2²×3²×7

• Divisors: Numbers that divide another number exactly, leaving no remainder. The divisors of 252 include 1, 2, 3, 4, 6, 7, 9, 12, and others.