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Which of the following expressions are factors of 12^17

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Director
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Which of the following expressions are factors of 12^17 [#permalink] New post 16 May 2018, 03:03
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Which of the following expressions are factors of \(12^{17}\)?

A. \((-2)^2\)\((-3)^4\)

B. \(12^3 + 12^3\)

C. \(4^{18}\)

D. \((2^{16})(3^{15})\)

E. \((3^{17})(4^{17})\)

F. \(12^{17} + 12^{17}\)
[Reveal] Spoiler: OA
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Re: Which of the following expressions are factors of 12^17 [#permalink] New post 24 May 2018, 09:59
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A B D E all are having factor either equal or less than 4^17 * 3^17

In C, 4^18 is given, which is more than 4^17. Hence it cannot be factor. Same with option E. 12^17 + 12^17 = 2(12^17). Here 2 is additional. Hence it also cannot be factor.
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Re: Which of the following expressions are factors of 12^17 [#permalink] New post 16 Nov 2018, 14:12
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Answers: A,B,D,E
12^17 = (3 * 4)^17 = 3^17 * (4)^17 = 3^17 * (2^2)^17 (2 can be -2 also and we can have even numbers of -3 as well)
So A can be true.
B : Here we should change it in multiplication form, it equals 2*12^13 which is a factor of 12^17
C is not true because the maximum power for 4 is 17
D can be true
E is true
F is not true. Here we should change it in multiplication form, which it will be 12^17+12^17 = 2^12^17 which is not a factor of 12^17
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Re: Which of the following expressions are factors of 12^17   [#permalink] 16 Nov 2018, 14:12
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Which of the following expressions are factors of 12^17

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