Question

The product of two consecutive natural numbers is always,
(a) an even number
(b) an odd number
(c) a prime number
(d) divisible by 3

Answer 1

Hint: Assume a variable n which will represent any natural number. In the question, we have to comment on the nature of the product of two consecutive natural numbers. The natural number which will be consecutive to n will be n+1. Try to substitute different n in the product of n and n+1 and try to find the nature of this product.

Complete step-by-step answer:
Before proceeding with the question, we must know the concept that will be required to solve in this question.
In number theory, if we do the product of an odd and an even number, the product of these two numbers will always be even.
Let us assume that n is one of the consecutive natural numbers. So, we can say the other consecutive natural number will be n+1. In the question, we have to comment on the nature of the product of these two consecutive numbers. The product of these two numbers will be given by,
n (n+1)
If we take n as an odd number, we can say that n+1 will be an even number. Since we have to find the product of an odd and an even number, we can say that the product will be even.
Similarly, if we take n as an even number, we can say that n+1 will be an odd number. Since we have to find the product of an odd and an even number, we can say that the product will be even.
So, from the above two paragraphs, we can say that the product of two consecutive natural numbers will always be an even number.
Hence, the answer is option (a).

Note: There is an alternate method to solve this question. This question can also be done by taking different integer values of n and then finding the nature of the product n (n+1).