A number is divisible by 4 if its last two digits form a number divisible by 4.
A number is divisible by 9 if the sum of its digits is divisible by 9.
Divisible by 6? It must pass both rules: be Even (div by 2) AND sum to a multiple of 3.
Look at the last three digits. If they form a number divisible by 8, the whole number is!
You've unlocked the secrets of 4, 6, 8, and 9. Now you can slice through numbers like a math ninja!