OK, this was part of an explanation for a Official Guide problem (but I know I can't post the question, so I won't)....

The explanation was that if x^3 is divisible by 9, then x MUST BE divisible by 3.

Is this because we know that x^3 has 3^2 as a factor, and because x is the only source of factors, x must have at least one three as a factor?

So would this hold true for something like x^9 is divisible by 9, so x MUST BE divisible by 3?

I'm just trying to understand the theory as to why this is true and under what circumstances it's true.

Thanks!

mdh

For any 'x' to be divisible by 9, it 'MUST' be divisible by 3 twice. Thus, any number divisible by 9 will always be divisible 3.
There are also a few rules in the numbers strategy guide or so. Hope this helps.

Yep, you guys have got it. If a number X is divisible by some other number Y, then X is also divisible by all of the factors of Y.