Question

Prove that the product of 3 consecutive positive integers is divisible by 6​

Answer 1

Answer:

Let three consecutive positive integers be, n, n + 1 and n + 2. Whenever a number is divided by 3, the remainder obtained is either 0 or 1 or 2. ... If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3. So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.