The divisibility rule for three is simple: a number is divisible by three if its digits add up to a multiple of three.

For example: 456 is divisible by 3, because 4 + 5 + 6 = 15, which is divisible by 3. (Just for fun, if you didn't know whether 15 was divisible by 3, you could add its digits: 1 + 5 = 6, which is divisible by 3.)

Similarly, 455 is not divisible by 3, because 4 + 5 + 5 = 14, which is not a multiple of 3.

The divisibility rule for six straightforward: a number is divisible by 6 if it is divisible by both 3 and 2.

Thus, 714 is a multiple of 6, because it is even and 7 + 1 + 4 = 12, which is a multiple of 3.

Finally, the divisibility rule for 9 is similar to the 3 rule: a number is divisible by 9 if its digits add to a multiple of 9. You may have already noticed this rule for small multiples of 9: 19, 27, 36, etc; their digits all add up to 9. But it also works for larger numbers. 1,908 is a multiple of 9 because 1 + 9 + 0 + 8 = 18, which is a multiple of 9.