Question

Prove that the product of three consecutive positive integer is divisible by 6.

Answer 1

To Prove: the product of three consecutive positive integers is divisible by 6.

Proof: Let n be any positive integer.

Since any positive integer is of the form 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4, 6q + 5

If n = 6q

, which is divisible by 6

If n = 6q + 1

Which is divisible by 6

If n = 6q + 2

Which is divisible by 6

Similarly we can prove others.

Hence it is proved that the product of three consecutive positive integers is divisible by 6.