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# What is the greatest prime factor of 3^6 - 1 ?

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Manager
Joined: 30 May 2013
Posts: 108
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 14 [0], given: 58

What is the greatest prime factor of 3^6 - 1 ? [#permalink]  01 Sep 2013, 17:59
00:00

Difficulty:

25% (low)

Question Stats:

63% (01:34) correct 36% (00:58) wrong based on 41 sessions
What is the greatest prime factor of 3^6 - 1 ?

A. 2
B. 3
C. 7
D. 13
E. 17
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Feb 2014, 02:35, edited 1 time in total.
Edited the question.
Intern
Joined: 31 Jan 2013
Posts: 17
Schools: ISB '15
WE: Consulting (Energy and Utilities)
Followers: 0

Kudos [?]: 12 [0], given: 18

Re: What is the greatest prime factor of the number (3^6 - 1) ? [#permalink]  01 Sep 2013, 20:44
3^6-1 = (3^3)^2 -1 = (27^2)-1

Dividing (27^2)-1 by 13 will give us a reminder of 0 ( Hint: (2*13+1)^2-1/13 = (Reminder 1)-1=0

Hence the greatest prime factor must be 13.

/SW
Math Expert
Joined: 02 Sep 2009
Posts: 16915
Followers: 2779

Kudos [?]: 17673 [2] , given: 2235

Re: What is the greatest prime factor of the number (3^6 - 1) ? [#permalink]  01 Sep 2013, 21:00
2
KUDOS
Expert's post
rrsnathan wrote:
What is the greatest prime factor of the number (3^6 - 1) ?
a) 2
b) 3
c) 7
d) 13
e) 17

Apply a^2-b^2=(a-b)(a+b).

3^6 - 1=(3^3-1)(3^3+1)=26*28=(2*13)*(2^2*7) --> the greatest prime factor is 13.

_________________
Re: What is the greatest prime factor of the number (3^6 - 1) ?   [#permalink] 01 Sep 2013, 21:00
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