Is 2137 a prime number?

The number 2137 has 4 factors that can divide the number completely without leaving any remainder. Thus, the number 2137 is a non-prime number. The factors of 2137 include 1, 3, 7, and 2137.

A number to be a prime number should follow the criteria that it should not have more than 2 factors. Here, 2137 has more than 2 factors, making it a composite number.

Given below are a few ways that can be 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
    

For the counting divisors method, we check whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 2137 would simply be:

Divisors of 2137 = 1, 3, 7, 2137
Number of divisors = 4

The number 2137 can be considered composite.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot divide it by any prime number, then it is considered a prime number.

In the divisibility method, prime numbers only have 2 divisors: 1 and themselves.

The divisors of 2137 are 1, 3, 7, and 2137.

Thus, 2137 consists of 4 factors that divide it completely without any remainder.

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

The list of prime numbers under 100 are:
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

2137 is not present in the list, meaning it is not a prime number.
 

This method is used for a non-prime/composite number. Since 2137 is a composite number, the prime factorization of 2137 is:

Factors of 2137 = 3 × 7 × 101
 

• Prime Number: A prime number is a natural number greater than 1 that has only two distinct divisors: 1 and itself. Example: 2, 3, 5, 7.

• Composite Number: A composite number is a natural number greater than 1 that has more than two divisors. It is not prime. Example: 6, 8, 2137.

• Divisors: Divisors are numbers that divide another number exactly, without leaving a remainder. For example, divisors of 2137 are 1, 3, 7, and 2137.

• Prime Factorization: Prime factorization involves breaking down a number into its prime factors. For example, the prime factorization of 2137 is 3 × 7 × 101.

• Divisibility Test: A divisibility test is a method used to determine if a number can be divided by another number without leaving a remainder. For 2137, dividing by 3, 7, and other primes reveals it is not prime.