identifying multiples of 9 (nine)

I was given a simple method to identify multiples of 9 in grade school.

Given a number, it is a series of digits d_1d_2d_3...d_n.

Add up all the digits \sum_{i=1}^nd_i.

If the resulting number is a multiple of nine (repeat the process if it has more than one digit), or is nine, then the original number is a multiple of nine.

For example, take 81, it is the digits 8 and 1, add the digits, 8 + 1, the result is 9, therefore 81 is a multiple of 9.

For another example, take 123456, it is the digits 1, 2, 3, 4, 5, and 6, add the digits, 1 + 2 + 3 + 4 + 5 + 6, the result is 21, which is multiple digits, add the digits, 2 + 1, the result is 3, therefore 123456 is not a multiple of 9.