Is 31 a prime number?

Every real number is classified into two parts: prime or composite numbers.

The number 31 is a prime number, and in prime factorization of 31, the result will be only one and thirty-one as the factors of 31.

And the number 31 has exactly two factors, that is one and itself, it is considered as a prime number.

For a number to be prime, it has to satisfy the below conditions; 

• The number should have only 2 divisors 

•  The factors should be number 1 and itself only.

Listed below are some methods to find out whether a particular number is prime or not;

• Counting Divisors Method

• Divisibility Test Method

• Prime Number Chart

• Prime Factorization 
   

In the counting divisors method, we list the divisors of the given number and check if the number, to be considered prime, satisfies the two conditions.

The counting divisors method for 31 would simply be:

• Divisors of 31 = 1, 31.

• Number of divisors = 2

The number 31, hence, can say to be prime. 
 

In this method, the prime number only has two divisors, which are one and themselves.

Hence, there is no any divisibility test for the number 31 other than checking if it is divisible by one and thirty-one. 
 

List the prime number chart up to 40. 

The prime numbers from 1 to 40 are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

By keeping a note of the chart like above, we can easily realize a number is prime or not. 
 

Prime factorization is only applicable to non-prime numbers/composite numbers. As long as 31 has no other factor than 1 and 31, it has no option to factored into smaller prime numbers.
 

• Prime Number: A number which has only 2 divisors, out of which is 1 and the other is the number itself.

• Composite Number: A number that can be prime factorized further, or a number that holds divisors other than one and itself. 

• Prime Factorization: Splitting down a number into its smaller factors is said to be a prime factorization.