For divisibility by any number that you haven't memorized a shortcut rule for, consider all the factors of that number and pick out a pair of two factors for which:

a. you know a divisibility rule AND;

b. their least common multiple is the number itself

Here are some examples for those numbers:

36's factors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Well, 4*9 = 36 and their LCM is 36 so you have something to work with here. Check if the number is divisible by 4 and 9 and if it is, then it is divisible by 36 as well.

32's factors are 1, 2, 4, 8, 16, 32. However, since the only prime factor of 32 is 2, there is no pair of factors for which the LCM is 32 (besides 32 and 1) so there is no shortcut divisibility rule for 32.

24's factors are 1, 2, 3, 4, 6, 8, 12, 24. Well, 8*3 = 24 and their LCM is 24. Therefore, if the number is divisible by both 8 and 3, it's divisible by 24.