It is well-known that an integer is divisible by 9 if and only if the sum of its digits in base-10 is divisible by 9. But this is only a part of the story. The proof of this fact leads to a more general result, which is that the residue class of an integer is the same as the residue class of the sum of its digits modulo 9. We prove this fact in this video using modular arithmetic. From it, we can deduce a similar theorem for divisibility by 3.