It is currently 21 Oct 2017, 18:48

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

prime factor problem

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 28 Jun 2008
Posts: 45

Kudos [?]: 135 [0], given: 31

prime factor problem [#permalink]

Show Tags

New post 09 Jun 2009, 20:46
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hey guys was wondering if anyone could offer a good way to do this problem:

What is the greatest prime factor of 4*17-2*28? (by * I mean raised to the 17th power and raised to the 28th power.)

A. 2
B. 3
C. 5
D. 7
E. 11

Answer: D.

Kudos [?]: 135 [0], given: 31

1 KUDOS received
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 305 [1], given: 3

Location: Next to Google
Schools: Haas School of Business
Re: prime factor problem [#permalink]

Show Tags

New post 09 Jun 2009, 23:19
1
This post received
KUDOS
\(4^{17}-2^{28}\)

\(=2^{2^{17}}-2^{28}\)

\(= 2^{34}-2^{28}\)

\(= 2^{28}\times2^6-2^{28}\)

\(=2^{28}(2^6-1)\)

\(=2^{28}(64-1)\)

\(=2^{28}(63)\)

\(=2^{28}\times 7 \times 3 \times 3\)

Hence the largest prime factor is 7 i.e. answer is D

Kudos [?]: 305 [1], given: 3

Intern
Intern
avatar
Joined: 28 Jun 2008
Posts: 45

Kudos [?]: 135 [0], given: 31

Re: prime factor problem [#permalink]

Show Tags

New post 10 Jun 2009, 10:14
Hi and thanks for your help. I understand how you got to 2*28x7x3x3 but I dont quite understand why seven is definitively the largest prime factor. Couldnt 2*28 have a prime factor larger than 7?

Kudos [?]: 135 [0], given: 31

1 KUDOS received
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 305 [1], given: 3

Location: Next to Google
Schools: Haas School of Business
Re: prime factor problem [#permalink]

Show Tags

New post 10 Jun 2009, 10:24
1
This post received
KUDOS
A Prime factor is a number that can be divided evenly only by 1, or itself.

\(2^{28} = 2 \times 2 \times 2 \times 2 \times 2 .....28 times.\)

Hence here the largest prime factor here is just 2 as any other factor such as 8

\(2\times 2\times 2 = 8\)

is divisible by 1,2,4 and 8. Hence it is not prime. The only prime factor in \(2^{28}\) is 2.

So overall the largest prime factor is 7.

Kudos [?]: 305 [1], given: 3

Re: prime factor problem   [#permalink] 10 Jun 2009, 10:24
Display posts from previous: Sort by

prime factor problem

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.