Does this rule about factors and exponents ALWAYS hold true?

[mdh3000]

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

[Success]

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.

[StaceyKoprince]

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.