If 9 divides 2x, does 9 divide x?

[rg2004]

if 9 divides 2x does that imply 9 divides x? if so why?

thanks

 

[rg2004]

actually i found it.

"if a divides bc, and a and b are coprime, then a divides c"

 

[Office_Shredder]

The reason why has to do with primes. 9=3*3 so 3*3 divides 2x. This means that in the prime factorization of 2x, there have to be two 3's involved. Obviously neither comes from the 2 so both must come from the x