you might want to look at this website that pretty much explains it all nicely :
Math Forum: Explaining the Divisibility Rules
It is really a property of our positional notation system.
If a number is divisible by 3 then if the sum of its digits is divisible by 3.
Why is this true. I know it has something to with modulus...
I'm asking because I don't want to just memorize each rule, I wan to be able to just figure it out...