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# Which of the following expressions are factors of 12^17

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Director
Joined: 07 Jan 2018
Posts: 642
Followers: 7

Kudos [?]: 593 [1] , given: 88

Which of the following expressions are factors of 12^17 [#permalink]  16 May 2018, 03:03
1
KUDOS
00:00

Question Stats:

55% (01:06) correct 45% (00:50) wrong based on 20 sessions
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
Intern
Joined: 05 Jan 2018
Posts: 32
Followers: 0

Kudos [?]: 16 [1] , given: 8

Re: Which of the following expressions are factors of 12^17 [#permalink]  24 May 2018, 09:59
1
KUDOS
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.
Manager
Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 109 [1] , given: 22

Re: Which of the following expressions are factors of 12^17 [#permalink]  16 Nov 2018, 14:12
1
KUDOS
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
_________________

Re: Which of the following expressions are factors of 12^17   [#permalink] 16 Nov 2018, 14:12
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