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# Prime factor

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Manager
Joined: 05 Nov 2005
Posts: 223

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Location: Germany
Prime factor [#permalink]

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20 Dec 2005, 08:59
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How to solve this?

What is the greatest prime factor of 4^17 - 2^28 ?

(a) 2
(b) 3
(c) 5
(d) 7
(e) 11

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Senior Manager
Joined: 09 Aug 2005
Posts: 281

Kudos [?]: 5 [0], given: 0

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20 Dec 2005, 09:14
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

Answer 7

D

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Manager
Joined: 05 Nov 2005
Posts: 223

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Location: Germany

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20 Dec 2005, 09:21
I am not that fast, can you eludcidate please?

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Director
Joined: 17 Dec 2005
Posts: 544

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Location: Germany

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20 Dec 2005, 09:50
4^17 - 2^28 = 4^17 - 4^14 = 4^14 (4^3 - 1), thats the key

4^14 will have the smallest prime possibble 2, but

4^3 - 1 = 63 = 7*3*3, so the greatest prime is 7

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Current Student
Joined: 29 Jan 2005
Posts: 5201

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20 Dec 2005, 10:00
old_dream_1976 wrote:
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

Answer 7

D

Nice.....

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Senior Manager
Joined: 05 Oct 2005
Posts: 485

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20 Dec 2005, 11:02
Good job old dream... I agree w/ 7

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VP
Joined: 06 Jun 2004
Posts: 1050

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Location: CA

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20 Dec 2005, 12:50
Yup, agree with old dream's working. 7 it is
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

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Senior Manager
Joined: 03 Nov 2005
Posts: 380

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Location: Chicago, IL

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20 Dec 2005, 13:58
4^17 - 2^28 ===>2^34*2^28

==>2^28(2^6-1)

==>2^28*64-1

==>2^28*7*3^2

D stands
_________________

Hard work is the main determinant of success

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SVP
Joined: 16 Oct 2003
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20 Dec 2005, 19:55
2^28(2^6 - 1)
2^26*63
2^26*21*3
2^26*7*3*3
7 is the greatest prime factor.

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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

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Location: Singapore

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20 Dec 2005, 20:04
You will notice 4^17 = 2^34. So the question becomes 2^34 - 2^28 = 2^28(2^6-1) = 2^28(63)

The prime factors are 2^28 * 3 * 21 = 2^28 * 3 * 3 * 7

Greatest prime factor = 7

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Senior Manager
Joined: 15 Apr 2005
Posts: 414

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Location: India, Chennai
Re: Prime factor [#permalink]

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23 Dec 2005, 01:46
sandalphon wrote:
How to solve this?

What is the greatest prime factor of 4^17 - 2^28 ?

(a) 2
(b) 3
(c) 5
(d) 7
(e) 11

= 2^34 - 2^28
= 2^28(2^6-1)
= 2^28 (64-1)
= 2^28 * 63
= 2 ^28 * 7 * 9
= 2^ 28 * 7 * 3^2
So 7 is the greatest prime factor.

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

Re: Prime factor   [#permalink] 23 Dec 2005, 01:46
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# Prime factor

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