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

Given:

"Product of three consecutive positive integers is divisible by 6".

To do:

We have to find whether the given statement is true or false.

Solution:

Let three consecutive numbers be $a\ -\ 1$, $a$ and $a\ +\ 1$.

So,

Product $=\ (a\ -\ 1)\ \times\ (a)\ \times\ (a\ +\ 1)$

Now,

We know that in any three consecutive numbers:

- One number must be even, and the product is divisible by 2.

- One number must be multiple of 3, and the product is divisible by 3 also.

If a number is divisible by 2 and 3 both then that number is divisible by 6.

Therefore, the product of three consecutive positive integers is divisible by 6.

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