Divisibility

To test for divisibility by 3 and 9 we add up the digits of a number and see if the sum is divisible by 3 or 9. Does this work for 27 as well?

The tests work for 3 and 9 because:
10 = 1 (mod 3)
10 = 1 (mod 9)
mod means that:
10 = 1+3a, for some a (3)
10 = 1+9a, for some a (1)

It doesn't work for 27,
10 != 1 (mod 27)

A test for divisibility by 27 would be:
- check for divisibility by 3
- divide by 3
- check for divisibility by 9