Question

Is \[31\] a prime or composite number?

Answer 1

Hint: We have to state whether the given number is a prime number, a composite number or neither. We solve this question using the concept of the definition of prime numbers and composite numbers. We should also have the knowledge of how to split a number into its prime factors. First, we will split the given number into its prime factors and then using the definition of the prime numbers and composite number we will state that the number is prime number, composite number or neither.

Complete step-by-step answer:
Given:
The number is \[31\]
Prime numbers: A number which is only divisible by only two numbers i.e. \[1\] and the number itself. In simple terms the number can’t be split into its factors.
Composite numbers: A number which is divisible by more than two numbers i.e. other numbers than \[1\] and the number itself. In simple terms, a number which can be represented in terms of other numbers.
Now, we will split the given number into its prime factor.
Now, splitting the number we can write the given number as:
\[31 = 31 \times 1\]
As, the given number has only two possible factors i.e. \[1\] and the number itself. Therefore, we can say that the given number is a prime number.
Hence, \[31\] is a prime number.
So, the correct answer is “prime number”.

Note: For splitting a number into its prime factors, we do it by checking the divisibility of the number by some of the starting prime numbers like \[2,3,5,7,11,13....\] in most of the cases we will get a factor of the given number from these numbers only. If not so then we check the possibility for greater prime numbers.