Question

Find the counterexample of the statement “Every natural number is either prime or composite”.
A. 5
B. 1
C. 6
D. None of these

Answer 1

Hint: In this question, we will check that which natural number does not have two or more than two factors. And categories these numbers as prime and composite numbers and check the same for 1. In this way we can see that numbers are either prime or composite.

Complete step-by-step answer:
A Prime number is a positive integer having exactly two factors. Prime numbers are the numbers, which are divisible by 1 or by the number itself. But, 1 is not a prime number because it does not have two factors.
A composite number is the number which has more than two factors, those numbers are also called composite numbers. But, 1 is not a composite number because the only divisor of 1 is 1.
1 is neither a prime number nor a composite number

So, the correct answer is “Option B”.

Note: Here, we have some important properties of Prime numbers are as follows:
*Every number which is greater than 1 can be divided by at least one prime number.
*Every even positive integer greater than 2 can be expressed as the sum of two primes.
*All the other prime numbers are odd, except 2. 2 is the only even prime number.
 The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 29. But 1 is a non-prime number.
 One is considered as neither a prime nor a composite number because it does not have any factor other than 1.