# 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

Last updated date: 24th Mar 2023

•

Total views: 211.4k

•

Views today: 4.88k

Answer

Verified

211.4k+ views

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).

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).

Recently Updated Pages

Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?