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# Which of the following is NOT a prime factor of (5^6−2^6)?

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Manager
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Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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19 Jan 2014, 01:15
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Which of the following is NOT a prime factor of (5^6−2^6)?

A. 3
B. 7
C. 13
D. 17
E. 19
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Jan 2014, 09:21, edited 1 time in total.
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Re: Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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19 Jan 2014, 09:25
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Mountain14 wrote:
Which of the following is NOT a prime factor of (5^6−2^6)?

A. 3
B. 7
C. 13
D. 17
E. 19

Apply $$a^2-b^2=(a-b)(a+b)$$: $$5^6-2^6=(5^3-2^3)(5^3+2^3)=117*133=(3^2*13)(7*19)$$. From the options only 17 is not a prime factor of 5^6−2^6.

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Re: Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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19 Jan 2014, 22:45
1
KUDOS
Which of the following is NOT a prime factor of $$(5^6 - 2^6)?$$

A. 3
B. 7
C. 13
D. 17
E. 19

$$(5^6 - 2^6)$$
$$=(5^3 - 2^3)(5^3 + 2^3) =(5-2)(5^2+5*2+2^2)(5+2)(5^2-5*2+2^2) =3*39*7*19 =3*3*13*7*19$$

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Which of the following is NOT a prime factor of (5^6−2^6) ? [#permalink]

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31 Jul 2015, 11:05
4
KUDOS
Which of the following is NOT a prime factor of (5^6−2^6) ?

a)3
b)7
c)13
d)17
e)19

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Re: Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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31 Jul 2015, 11:16
Gmat1008 wrote:
Which of the following is NOT a prime factor of (5^6−2^6) ?

a)3
b)7
c)13
d)17
e)19

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Re: Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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06 Aug 2017, 16:05
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Re: Which of the following is NOT a prime factor of (5^6−2^6)? [#permalink]

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10 Aug 2017, 10:45
HarveyS wrote:
Which of the following is NOT a prime factor of (5^6−2^6)?

A. 3
B. 7
C. 13
D. 17
E. 19

Let’s simplify the given expression:

5^6 − 2^6 = (5^3 + 2^3)(5^3 - 2^3) = (125 + 8)(125 - 8) = (133)(117) = (7 x 19) x (3 x 3 x 13)

We see that the only answer choice that divides into (133)(117) is 17.

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Re: Which of the following is NOT a prime factor of (5^6−2^6)?   [#permalink] 10 Aug 2017, 10:45
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