Question

Is \[36\] a prime or composite number?

Answer 1

Hint: We have to find whether \[36\] is a prime number or composite number. For that, we will first recall the definitions of prime numbers and composite numbers. After that we will write down the factors of \[36\] and analyse which category \[36\] belongs to, a prime number or a composite number.

Complete step-by-step answer:
In mathematics, two types of numbers exist that rely on the factors they have. These two types of numbers are prime numbers and composite numbers.
So, first let’s recall the definition of the prime numbers and composite numbers.

Prime numbers are those numbers which have only two factors i.e., one and itself. It implies that the number can be divided only by \[1\] and itself, which also means it has no other divisor except \[1\] and the number itself.

On the contrary, composite numbers are opposites of prime numbers. These are those numbers which have more than two factors. It implies that the number can also be divided by any other numbers except one and itself. Composite numbers are also defined as the integers which can obtained by multiplying the two smallest positive numbers and included one divisor other than \[1\]

Now, we have to find whether \[36\] is a prime number or composite number.
To determine whether \[36\] is a prime number or composite number, first of all we need to write down its factors.
So, the factors of \[36\] are \[1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}6,{\text{ }}9,{\text{ }}12,{\text{ }}18,{\text{ }}36\]
Now, we will analyse which category \[36\] belongs to.
Since, \[36\] has more than two factors and we know that for a number to be classified as a prime number, it should have exactly two factors. So, we can say that \[36\] is not a prime number.
Now, as \[36\] has more than two factors, and we know that for a number to be classified as a composite number, it should have more than two factors. So, we can say that \[36\] is a composite number.
Hence, we get the result as \[36\] is a composite number.
So, the correct answer is “composite number”.

Note: Students must note that there is no defined formula to find whether the number is prime or composite, apart from finding its factors. Also, we can define prime numbers as the positive numbers which are not a product of two positive integers other than itself. Another point to note is that \[0{\text{ }}and{\text{ }}1\] are the only two numbers which are neither prime nor composite.