Explanation

Given n(n + 1)(n + 5):

1. n(n + 1) is always even (multiple of 2) since it's the product of two consecutive integers.

2. For divisibility by 3:

    If n is a multiple of 3, the expression is divisible by 3.

    If n = 3k + 1, then n + 5 = 3k + 6 is divisible by 3.

    If n = 3k + 2, then n + 1 = 3k + 3 is divisible by 3.

Given these cases, n(n + 1)(n + 5) is divisible by 3.