Something's a multiple of 3 if the digits add up to a multiple of 3. Any other rules?

E.g. 123 is a multiple of 3 because 1+2+3=6 and 6/2 = 3.
I'm doing the Intermediate Maths Challenge tomorrow and am just wondering if there are any similar tricks for other numbers that would come in handy. Or any tips in general.

For that one, just have a search for divisibility rules (9,11,...)
Tbh, at this stage, maybe try a paper tonight (or chill) rather than trying to learn new stuff.

This video from Vsauce covers all of the divisibility rules.

You can find others on the internet too.

Same for 9 (multiple of 9 if the digit sum is).

If you alternate adding / subtracting digits, then you have a multiple of 11 if and only if the sum is a multiple of 11. E.g. 165 becomes 1 - 6 + 5 = 0 so is a multiple of 11.

Not strictly a division rule, but it's worth knowing that 1001 = 7 x 11 x 13. So, for example, any number of the form ABCABC (e.g. 123123) will be divisible by 1001 and so by 7, 11 and 13.