Does 9 Divide X? Reasons Explained

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The discussion centers on the divisibility rule involving the number 9 and its relation to the variable x. It establishes that if 9 divides 2x, then 9 must also divide x, based on the principle that if a divides bc and a and b are coprime, then a divides c. The reasoning is rooted in prime factorization, specifically that 9, which is 3 squared, requires two factors of 3 to be present in the factorization of 2x, both of which must originate from x since 2 does not contribute any factors of 3.

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rg2004
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if 9 divides 2x does that imply 9 divides x? if so why?

thanks
 
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actually i found it.

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

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