Question

Find the truth value
Neither 21 is a prime number nor is it divisible by 3.

Answer 1

Hint – In this particular question use the concept that prime numbers are those numbers which are divisible by either 1 or itself and these numbers have no common factors except 1 so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Prime numbers
Prime numbers are those which have no common factors except one (1), i.e. the factors of the prime numbers is either 1 or itself, so these numbers are called prime numbers.
For example: 5
As we know that 5 is not divisible by any number except 1 and itself so 5 is a prime number.
Even numbers cannot be prime numbers as even numbers are divisible by 2, but 2 is a prime number as well as even number this is a special case of even prime number.
So prime numbers are odd numbers but all odd numbers are not prime numbers only those odd numbers which are divisible by either 1 or itself are called odd prime numbers.
So there is only one even prime number and the remaining are odd prime numbers.
So the set of prime numbers are given below,
A = {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, etc.}
So as we see that 21 is not listed in the above set, so 21 is not a prime number.
Now factorize the 21 we have,
$ \Rightarrow 21 = 1 \times 3 \times 7$
So as we see that the factors of 21 are 1, 3 and 7.
Therefore, 21 is divisible by 3.
So 21 is not a prime number and it is divisible by 3.
So the given question statement is false.
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that Even number cannot be prime numbers as even numbers are divisible by 2, but 2 is a prime number as well as even number this is a special case of even prime number, So prime numbers are odd numbers but all odd numbers are not prime numbers only those odd numbers which are divisible by either 1 or itself are called as odd prime numbers.