Question

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

Answer 1

Let the three consecutive numbers be n, n + 1 and n + 2.

Whenever a number is divided by 3, the remainder obtained is 0, 1, or 2.

Therefore, n = 3p or n = 3p + 1 or n = 3p + 2, where p is any natural number.

Now,
If n = 3p, then n is divisible by 3

If n = 3p + 1
⇒ n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1), then (n + 2) is divisible by 3

If n = 3p + 2
⇒ n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1), then (n + 1) is divisible by 3

Thus, we can say that one of the three numbers n, n + 1, n + 2 is always divisible by 3.

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