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# The number 18^5 is NOT divisible by:

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Intern
Joined: 31 Jan 2018
Posts: 9
The number 18^5 is NOT divisible by:  [#permalink]

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03 Feb 2018, 21:09
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:11) correct 31% (01:15) wrong based on 55 sessions

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The number 18^5 is NOT divisible by:

A. 32
B. 60
C. 108
D. 144
E. 324
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: The number 18^5 is NOT divisible by:  [#permalink]

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03 Feb 2018, 22:03
ggpapas wrote:
The number 18^5 is NOT divisble by:
A.32
B.60
C.108
D.144
E.324

18^5= 2^5*9^5=2^5*3^10..

We can check the factors of choices now..
But clearly 5 is not a factor of 18^5, so 60 cannot evenly divide it..

B
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Re: The number 18^5 is NOT divisible by:  [#permalink]

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04 Feb 2018, 09:43
ggpapas wrote:
The number 18^5 is NOT divisible by:

A. 32
B. 60
C. 108
D. 144
E. 324

In order to solve these kind of problems, we need to prime factorize
the number and the answer options.

Since we have been asked to check which answer option is not divisible,
we would have to find an answer option which on prime-factorization
contains a factor which does not divide the number

Number(when prime factorized) - $$18^5 = (2*3^2)^5 = 2^5 * 3^{10}$$

A. $$32 - 2^5$$
B. $$60 - 2^2 * 3 * 5$$
C. $$108 - 2^2 *3^3$$
D. $$144 - 2^4 * 3^2$$
E. $$324 - 2^2 *3^4$$

Since 60 contains a 5 which is not present in the number, it will not divide(Option B)
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Re: The number 18^5 is NOT divisible by: &nbs [#permalink] 04 Feb 2018, 09:43
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