Question

One of the three consecutive positive integers is always divisible by ______.

Answer 1

One of the three consecutive positive integers is always divisible by 3.

Explanation:

Let the three consecutive positive integers be n, n + 1, n + 2. Considering n mod 3, n is either 0, 1 or 2 mod 3. If n ≡ 0 (mod 3) then n is divisible by 3; if n ≡ 1 (mod 3) then n + 2 ≡ 0 (mod 3); if n ≡ 2 (mod 3) then n + 1 ≡ 0 (mod 3). Hence one of the three is always divisible by 3.