Divisibility by 3
Add up the digits of the number. If the sum of the digits is divisible by three, then the number is as well.
For experts: Why does the 'divisibility by 3' rule work?
A 2 digit number can be written as:
10a + b = 9a +(a + b).
We know that 9a is divisible by 3, so 10a + b will be divisible by 3 if and only if (a + b) is divisible by 3 and (a + b) is the sum of the digits.
Similarly, 100a +10b + c = 99a + 9b + (a + b + c),
and 99a + 9b is divisible by 3, so the total will be if ( a + b + c) is divisible by 3.