Question

Which of the following is a composite number?
(a) 23
(b) 29
(c) 32
(d) None of these

Answer 1

Hint:
Here, we need to find the composite number from the given options. We will be using the divisibility rules to check which of the given options is a composite number or a prime number, and thus, find the correct option.

Complete step by step solution:
We will check all the options to find which of them is a composite number.
The first number is 23.
The prime numbers lower than 23 are 2, 3, 5, 7, 11, 13, 17, 19.
We can observe that 23 is not divisible by any of the prime numbers lower than 23.
Hence, 23 is not divisible by any number other than 1 and itself.
Therefore, 23 is a prime number.
Thus, option (a) is incorrect.
The second number is 29.
The prime numbers lower than 29 are 2, 3, 5, 7, 11, 13, 17, 19, 23.
We can observe that 29 is not divisible by any of the prime numbers lower than 29.
Hence, 29 is not divisible by any number other than 1 and itself.
Therefore, 29 is a prime number.
Thus, option (b) is incorrect.
The next number is 32.
We will check the divisibility by 2.
Every number that has the digit 2, 4, 6, 8, 0 in the unit’s place is divisible by 2. This means that all even numbers are divisible by 2.
The digit at the unit’s place of the number 32 is 2. 32 is an even number.
Hence, the number 32 is divisible by 2.
Since 32 is divisible by a number other than itself, it is a composite number.

Thus, the correct option is option (c).

Note:
Here, we need to keep in mind the definition of prime numbers and composite numbers to distinguish the numbers. Prime numbers are the numbers which have only two factors : 1 and the number itself. Composite numbers are the numbers that are not prime numbers and are divisible by factors other than 1 and themselves.