Is 631 a prime number?

The number 631 has several factors that can divide it completely without leaving any remainder. Thus, the number 631 is a non-prime number. The factors of 631 include 1, 17, 37, and 631.

A number to be a prime number should follow the criteria that it should not have factors other than 1 and itself. Here, 631 has more than 2 factors, 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 checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 631 would simply be:

Divisors of 631 = 1, 17, 37, 631
Number of divisors = 4

The number 631 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, a prime number only has 2 divisors, which are 1 and itself.

The divisors of 631 are 1, 17, 37, and 631.

Thus, 631 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, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

631 is not present in the list, which confirms it is not a prime number.
 

This method is only used for a non-prime number/composite number. Since 631 is a composite number, the prime factorization for 631 is:

Factors of 631 = 17 × 37
 

• Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers. 631, however, is not a prime number as it has more than two divisors.

• Composite Number: A number that has more than two divisors. In the case of 631, it is a composite number because its divisors include 1, 17, 37, and 631.

• Divisibility Test: A method used to determine if one number can be evenly divided by another. If a number can be divided by a smaller prime number without leaving a remainder, it is not prime. For 631, divisibility tests with 17 and 37 show that it is divisible by these numbers, proving it is not prime.

• Prime Factorization: Breaking down a composite number into its prime factors. The prime factorization of 631 is 17 × 37, as 631 can be divided into these prime numbers.

• Divisors: Numbers that can divide another number completely without leaving a remainder. For 631, the divisors are 1, 17, 37, and 631, indicating it is a composite number.