Est-ce que je suis un multiple de...?

Today in Math we reviewed how to determine if a number is a multiple of a specific digit.
For example, we know that numbers are multiples of 5 if the last digit is 5 or 0. Or, that a number is a multiple of 2 if it is an even number (a number ending in 0,2,4,6,8).

The challenge today was learning the 'trick' for multiples of 3 and 9. How do we know if a number is a multiple of 3 or 9 without actually counting by 3 or 9 all the way up to that number?

Test out your ideas with this set of numbers:

330       612       1003       919       450        3012         1027

What numbers are multiples of 3? 9? Is it possible for numbers to be multiples of both?