In order for a number to be divisible by 9, it must have 3 as a factor at least twice. Example 18 = 3*3*2 = 9*2, so 18/9 = 2 In order for a number to be divisible by 3, it must have 3 as a factor at least once. Example 15 = 3*5, so 15/3 = 5 A number having a factor of 3 exactly once will be divisible by 3, but not by 9. Such a number will have digits that add to a multiple of 3, but not a multiple of 9. Example 48 = (2^4)*3 digits add to 12, then 1+2 = 3. 12 (or 3) is not a multiple of 9, so the number is not divisible by 9. It is divisible by 3. 48/3 = 16. 48/9 = 16/3 = 5 1/3.
