Question

The number that is neither prime nor composite is?
(a) 0
(b) 1
(c) 2
(d) 3

Answer 1

Hint: First of all try to recollect the definition of prime numbers and composite numbers and all the numbers which come in these categories. Then choose the number which does come in both the categories as the number which is neither prime nor composite from the options.

Complete step-by-step answer:
Here we have to find the number which is neither odd nor even among the numbers 0, 1, 2 and 3.
Before proceeding with this question, let us see what prime numbers and composite numbers mean.
Prime numbers: Prime numbers are the positive integers having only two factors 1 and the integer itself. For example, factors of 8 are 1, 2, 4 and 8 which are four factors in total. But factors of 7 are only 1 and 7 totally two. Hence, 7 is a prime number but 8 is not. Smallest prime number is 2.
We can also say that the prime numbers are the numbers which are only divisible by 1 or the number itself.
Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc.
Composite numbers: Composite numbers are positive integers having factors other than 1 and the number itself. Composite numbers are the just opposite form of prime numbers that is any number which is not a prime number is a composite number. Smallest composite number is 4.
Some examples of composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 etc.
Now let us consider the numbers 0, 1, 2 and 3. Here, the numbers 2 and 3 are divisible only by 1 and itself so both of them are prime numbers.
Now, the numbers 0 and 1 are not considered as prime or composite because the only factors they have are themselves. As we have already seen, prime numbers have only 2 factors, 1 and itself. Composite numbers have more than 2 factors. 0 and 1 obeys neither of these rules because they have only 1 factor.
Hence, options (a) and (b) are the right answers.

Note: We can also say that positive integers which are not a product of two positive integers other than itself are prime numbers whole numbers which are products of two positive integers other than itself are composite numbers. Also, students must note that there is no defined formula to find if a number is prime or composite, apart from finding its factors.