This takes me back
Divisible by 3
Add the digits, and if that total is a multiple of 3, the original number is divisible by 3
547
5+4+7 = 16 which is not a multiple of 3, therefore 547 not divisible by 3
Multiple of 4
Any exact number of hundreds is a multiple of 4, so we only need to look at the last two digits -- if they are a multiple of 4, so is the full number
Multiple of 6
The EVEN multiples of 3 are multiples of 6
Multiple of 8
Any exact number of thousands is a multiple of 8, so we only need to look at the last three digits -- if they are a multiple of 8, so is the full number
35912
912 is an exact multiple of 8, so 35912 is a multiple of 8
(as are 36912, 6556565657744912, etc)
Multiple of 9
Add the digits, and if that total is a multiple of 9, the original number is divisible by 9
35568
3+5+5+6+8 = 27 which is a multiple of 9, therefore 35568 is a multiple of 9
Multiple of 11
The difference between the sums of the odd digits and the even digits is 0 or a multiple of 11
35915
3+9+5 = 17
5+1 = 6
difference 11
therefore 35915 is a multiple of 11