NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.2 - Short Answer Questions with Reasoning
Question 3

Question. 3

“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false? Justify your answer.

The statement is True. The product of three consecutive positive integers is always divisible by 6.

Step 1: Write the three consecutive integers.

Let the integers be \(n, n+1, n+2\).

Step 2: Check divisibility by 2 (even number).

Any three consecutive numbers must include at least one even number,

because every second number is even.

So, \(n(n+1)(n+2)\) is divisible by 2.

Step 3: Check divisibility by 3.

Every third number is divisible by 3, so among \(n, n+1, n+2\),

at least one will be a multiple of 3.

So, \(n(n+1)(n+2)\) is divisible by 3.

Step 4: Combine the results.

If a number is divisible by both 2 and 3, it is divisible by 6.

Hence, the product \(n(n+1)(n+2)\) is always divisible by 6.

Conclusion: The statement is True.