I just thought of another thing that's pretty useful but I do it so much I take it for granted. I suspect more people know this one than the sine approximation algorithm.

Numbers that end in 0, 2, 4, 6, or 8 are divisible by 2, and numbers that end in 0 or 5 or divisible by 5. Pretty common right?

Numbers that add up to 3, 6, or 9 are divisible by 3. For example 123456 becomes 1 + 2 + 3 + 4 + 5 + 6 = 21, 2 + 1 = 3, so 123456 is divisible by 3 (and it's 41152).

Numbers that are divisible by 3 and are even are divisible by 6. From the above, 123456/6 = 20576.

Numbers that add up to 9 are divisible by 9. And yes, this works for all numbers, not just 2-digit ones. Take 63423 for example. 6 + 3 + 4 + 2 + 3 = 18, 1 + 8 = 9, and 63423/9 = 7047.