Question

Prove that if n is a positive even integer, then 24 divides n(n+1)(n+2).

Answer 1

Given: n is a positive even integer

Now we know that one out of three consecutive integer is divisible by 3

⇒ 3 is a factor of n(n+1)(n+2)

also since n is even

∴ one out of n and (n+2) will have a factor 2 and the other will have a factor 4

Thus 2 × 4 = 8 is a factor of n(n+2) or n(n+1)(n+2)

Hence, 3 × 8 = 24 is a factor of n(n+1)(n+2)