Question

Which of the following is a composite number?
A) $23$
B) $29$
C) $32$
D) None of these

Answer 1

Hint:
Consider the factorisation of each number. If there are factors other than one and the number itself, it is a composite number. If not, it is a prime number.

Complete step by step solution:
We are given three numbers.
We have to identify the composite number among them.
Composite numbers are those numbers which have factors other than one and the number itself.
Numbers which are not composite are called prime.

Let us check each number one by one.
First number is $23$.
We can see that the unique factorisation of $23$ is $1 \times 23$. This gives $1$ and $23$ as the only factors of $23$.
Therefore $23$ is a prime number.
Next number is $29$.
We can see that the unique factorisation of $29$ is $1 \times 29$. This gives $1$ and $29$ as the only factors of $29$.
Therefore $29$ is a prime number.
The last number is $32$.
The number $32$ can be expressed as a product in different ways.
They are $1 \times 32,2 \times 16,4 \times 8$.
So $32$ is not a prime number. It has factors other than one and itself, which are $2,4,8$ and $16$.
This gives, $32$ is a composite number.

Therefore the answer is option C.

Note:
The number one has no any factors other than itself. But one is considered neither as a prime nor as a composite number. In fact, one is the only number which is not a prime or composite. Since every even number has two as a factor, we can clearly say that every even number is a composite number.