The easiest way is:
Add up all, the digits in the number. If their sum is divisible by 3,
then the number built with them is also divisible by 3.
Examples:
==> 144 . . . (1 + 4 + 4) = 9 ... 9 is divisible by 3, so 144 is too.
==> 623 . . . (6 + 2 + 3) = 11 ... 11 is not divisible by 3, so 623 isn't either.
