a number is divisible by
2 if it is even (the last digit is 0, 2, 4, 6, or 8)
3 if the sum of the digits is divisible by 3
4 if the last two digits are divisible by 4
5 if the last two digit is 0 or 5
6 if it is divisible by both 3 and 2
8 if the last three number are divisible by 8
9 if the sum of the digits is divisible by 9
10 if the last digit is 0
11 if the difference between the sums of alternating digits is 0 or multiples of 11