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Prove that the product of three consecutive positive integers is divisible by 6.
Given: Statement "Product of three consecutive positive integers is divisible by 6".
To prove: Here we have to prove the given statement.
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.
Updated on: 10-Oct-2022
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