Is 1937 a prime number?

The number 1937 has got 4 factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 1937 is a non-prime number. The factors of 1937 include 1,13, 149, and 1937.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 1937 has more than 2 factors, hence making it a composite number.

Given below are a few ways that can be used to find prime or composite numbers.

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, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 1937 would simply be:

Divisors of 1937 = 1,13, 149, 1937
Number of divisors = 4

The number 1937 can be considered composite.
 

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

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of 1937 are 1,13, 149, and 1937.

Thus, 1937 consists of 4 factors that divide it completely without any remainder.
 

The prime number chart is the 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.

1937 is not present in the list, it is not a prime number.
 

This method is only used for a non-prime number/composite number. Since 1937 is a composite number, the prime factorization for 1937 is:

Factors of 1937 = 13 × 149
 

• Prime Number: A number greater than 1 that has no divisors other than 1 and itself. For example, 2, 3, and 5 are prime numbers.

• Composite Number: A number that has more than two divisors. It is divisible by numbers other than 1 and itself, such as 1937, which can be divided by 1,13, 149, and 1937.

• Divisibility Test: A method used to check if a number is divisible by another number without a remainder. For instance, checking if 1937 is divisible by smaller prime numbers like 3, 5, or 7.

• Prime Factorization: Breaking down a composite number into its prime factors. The prime factorization of 1937 is 13 × 149, meaning it is a product of two prime numbers.

• Square Root Method: A method used to check divisibility by prime numbers up to the square root of the number. For 1937, the square root is approximately 44, so checking divisibility up to this number can help determine if it's prime.