basker561 wrote:

I'm new to this site so i'm probably posting in the wrong area. but i have a question that my book gave a horrible explanation on how to solve..

Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

the answer is 15 but all it says is 27^5= (3^3)^5 = 3^15 so 15 is the answer..

Can anyone explain this better? Also am i posting in the right area when i have questions like this?

Hi Basker!

For the above question, as the solution states \(27^5 = 3^15\)

Now \(3^x\) being a factor of\(3^15\) i.e \(3^x\) is to divide \(3^15\) with 0 remainder. If the question simply stated the possible range of x, the answer would be {0...15} The greatest value of the set is 15 and if x > 15, then it wouldn't be a factor anymore, it would become a multiple!

Hope this helps!

Regards,

Arpan

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