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Re: Which one of the following numbers is the greatest positive [#permalink]
Expert Reply
Please tag Divisibility/Factors/Multiples
thank you
basker561 wrote:
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19


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?
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Re: Which one of the following numbers is the greatest positive [#permalink]
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basker561 wrote:
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19


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?

27 = 3*3*3= 3^3
27^5 =(3^3)^5
=3^15
we have to find the greatest positive integer value for x
when x=15, it divides exactly once and that is the least positive integer value of the quotient
therefore, the correct option is D
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Re: Which one of the following numbers is the greatest positive [#permalink]
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basker561 wrote:
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19



Solution:

We see that 27^5 = (3^3)^5 = 3^15. Thus the greatest positive integer value of x such that 3^x is a factor of 27^5 is 15.

Answer: D
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Re: Which one of the following numbers is the greatest positive [#permalink]
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