Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Jul 2014, 07:32

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
User avatar
Joined: 25 Oct 2010
Posts: 46
WE 1: 3 yrs
Followers: 0

Kudos [?]: 15 [0], given: 13

What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 13 Nov 2010, 09:55
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

67% (01:34) correct 33% (00:46) wrong based on 350 sessions
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11
[Reveal] Spoiler: OA
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18718
Followers: 3239

Kudos [?]: 22316 [5] , given: 2613

Re: Factors [#permalink] New post 13 Nov 2010, 10:03
5
This post received
KUDOS
Expert's post
Manager
Manager
User avatar
Status: Planning to retake.
Affiliations: Alpha Psi Omega
Joined: 25 Oct 2010
Posts: 90
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q42 V37
GRE 1: 1310 Q630 V680
GPA: 3.16
Followers: 1

Kudos [?]: 13 [0], given: 14

Re: Factors [#permalink] New post 13 Nov 2010, 11:40
I have a hard time ignoring that 2^28 and trusting that breaking down 63 into its prime factors will give me the right answer.

Is there a hard and fast rule for why you can forget about 2^28 and trust that the 7 derived from 63 is correct?
_________________

Did I help you? Please give me kudos.

Each moment of time ought to be put to proper use, either in business, in improving the mind, in the innocent and necessary relaxations and entertainments of life, or in the care of the moral and religious part of our nature.

-William Andrus Alcott

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18718
Followers: 3239

Kudos [?]: 22316 [0], given: 2613

Re: Factors [#permalink] New post 13 Nov 2010, 11:47
Expert's post
rockzom wrote:
I have a hard time ignoring that 2^28 and trusting that breaking down 63 into its prime factors will give me the right answer.

Is there a hard and fast rule for why you can forget about 2^28 and trust that the 7 derived from 63 is correct?


4^{17}-2^{28} equals to 2^{28}*3^2*7, which means that the prime factors of this number are 2, 3, and 7, so the greatest prime factor is 7 (2^28=2*2*...*2, so this expression has only one prime: 2).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Status: Planning to retake.
Affiliations: Alpha Psi Omega
Joined: 25 Oct 2010
Posts: 90
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q42 V37
GRE 1: 1310 Q630 V680
GPA: 3.16
Followers: 1

Kudos [?]: 13 [0], given: 14

Re: Factors [#permalink] New post 13 Nov 2010, 12:05
I see. So essentially any time that you have an expression where all of the bases are prime, you can assume that the highest base would be the greatest prime factor?

For example, the expression 7^7 * 13^3 * 17 would have 17 as the greatest prime factor. Correct?
_________________

Did I help you? Please give me kudos.

Each moment of time ought to be put to proper use, either in business, in improving the mind, in the innocent and necessary relaxations and entertainments of life, or in the care of the moral and religious part of our nature.

-William Andrus Alcott

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18718
Followers: 3239

Kudos [?]: 22316 [1] , given: 2613

Re: Factors [#permalink] New post 13 Nov 2010, 12:10
1
This post received
KUDOS
Expert's post
rockzom wrote:
I see. So essentially any time that you have an expression where all of the bases are prime, you can assume that the highest base would be the greatest prime factor?

For example, the expression 7^7 * 13^3 * 17 would have 17 as the greatest prime factor. Correct?


How else? Exponentiation does not "produce" primes: if p is a prime number then p^12 or p^10000 will still have only one prime - p.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 08 Jun 2010
Posts: 172
Followers: 1

Kudos [?]: 5 [0], given: 10

Re: Factors [#permalink] New post 17 Jan 2011, 09:01
what A silly mistake.
I have solved it ,but in last I assume that I have to find the greatest n.m. of prime factors.not the n.m. itself
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1933
Followers: 465

Kudos [?]: 1841 [1] , given: 29

Re: what is the greatest prime factor? [#permalink] New post 05 Jun 2012, 14:22
1
This post received
KUDOS
Expert's post
Val1986 wrote:
What is the greatest prime factor of 4^17 - 2^28?

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

Is there a shortcut to solving this question? :?


I'm happy to help with this. :)

We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34

That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)

So, 4^17 - 2^28 = 2^34 - 2^28 = 2^(28 + 6) - 2^28 = (2^28)*(2*6) - 2^28 = (2^6 - 1) *(2^28)
= (64 - 1)*(2^28) = 63*(2^28)

The prime factors of 63 are 3*3*7, so the largest prime factor is 7, answer choice D.

Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/

Does all that make sense? Please let me know if you have any further questions.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Current Student
User avatar
Joined: 08 Jan 2009
Posts: 334
GMAT 1: 770 Q50 V46
Followers: 21

Kudos [?]: 76 [0], given: 7

GMAT Tests User
Re: what is the greatest prime factor? [#permalink] New post 05 Jun 2012, 14:24
4^17 - 2^28
= 2^34 - 2^28
= 2^28 * (2^6 - 1)
= (2*2*2*...) * (63)
= (2*2*2*...) * (3 * 3 * 7)

Greatest prime factor is 7
_________________

My Debrief

Manager
Manager
User avatar
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
GMAT 1: 660 Q V
GPA: 3.22
WE: Corporate Finance (Consulting)
Followers: 6

Kudos [?]: 17 [0], given: 16

Re: what is the greatest prime factor? [#permalink] New post 05 Jun 2012, 17:58
Val1986 wrote:
What is the greatest prime factor of 4^17 - 2^28?

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

Is there a shortcut to solving this question? :?


Answered this in 40 seconds (is that already considered a short cut? hehe)

= 4^17 - 2^28
= 2^[2(17)] - 2^28
= 2^34 - 2^28
= 2^28(2^6 - 1)
= 2^28(64-1)
= 2^28(63)

Now here comes the intuitive part
2^28 = greatest prime factor is 2
63 = 9 * 7 = 3 * 3 * 7 (prime factorization) = greatest prime factor is 7

Answer: (D)
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jan 2012
Posts: 304
Weight: 170lbs
GMAT 1: 730 Q48 V42
GMAT 2: 740 Q48 V42
WE: Analyst (Other)
Followers: 9

Kudos [?]: 60 [1] , given: 36

Re: what is the greatest prime factor? [#permalink] New post 05 Jun 2012, 23:41
1
This post received
KUDOS
mikemcgarry wrote:
Val1986 wrote:
What is the greatest prime factor of 4^17 - 2^28?

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

Is there a shortcut to solving this question? :?


I'm happy to help with this. :)

We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34

That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)

So, 4^17 - 2^28 = 2^34 - 2^28 = 2^(28 + 6) - 2^28 = (2^28)*(2*6) - 2^28 = (2^6 - 1) *(2^28)
= (64 - 1)*(2^28) = 63*(2^28)

The prime factors of 63 are 3*3*7, so the largest prime factor is 7, answer choice D.

Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/

Does all that make sense? Please let me know if you have any further questions.

Mike :)


Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
1 KUDOS received
Director
Director
User avatar
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 564
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Followers: 11

Kudos [?]: 122 [1] , given: 75

What is the greatest prime factor of [#permalink] New post 30 Aug 2012, 10:46
1
This post received
KUDOS
Let's simplify (4)^17-2^28
={(2)^2}^17-(2)^28
=(2)^34-(2)^28
=(2)^28{(2)^6-1}
=(2)^28{64-1}
=(2)^28{63}
=(2)^28{3x3x7}

clearly 7
_________________

" Make more efforts "
Press Kudos if you liked my post

Senior Manager
Senior Manager
User avatar
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 9

Kudos [?]: 62 [0], given: 31

GMAT Tests User
Re: What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 01 Oct 2012, 05:03
4^17 – 2^28
4^17 can be written as (2^2)^17 = 234
Therefore we get 2^34 - 2^28
Taking 22^8 as common we get 22^8 (26 – 1)

2^28 x 63

2^28 has only one prime factor ie. 2
63 has 3 x 3 x 7 as its prime factors …


Therefore all the factors of this product would be 2^28 x 3 x 3 x 7 ..

Thus 7 is the greatest factor (D)
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 123

Kudos [?]: 567 [1] , given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: What is the greatest prime factor of 4^17 - 2^28 [#permalink] New post 12 Nov 2012, 07:30
1
This post received
KUDOS
Expert's post
carcass wrote:
What is the greatest prime factor of 4^17 - 2^28?

(A) 2
(B) 3
(C) 5
(D) 7
(E) 11


4^17 can be written as 2^34.
Hence we have to find out the greatest prime factor of 2^34-2^28.
Take 2^28 as common.
2^28(2^6-1)
It will become, 2^28 * (64-1)
2^28 * 63
Greatest prime factor of 2^28=2
Greatest prime factor of 63 is 7.
2^28 * 7*9
Therefore the answer is 7.
Hence D
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Intern
Intern
User avatar
Joined: 03 Aug 2012
Posts: 17
Location: United States (OR)
Concentration: Finance, International Business
GPA: 3.53
WE: Analyst (Consumer Products)
Followers: 0

Kudos [?]: 8 [0], given: 6

CAT Tests
Re: What is the greatest prime factor of [#permalink] New post 12 Nov 2012, 11:04
thevenus wrote:

=(2)^34-(2)^28
=(2)^28{(2)^6-1}


I don't get the transition here... what's the process involved that these two equal one another??
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18718
Followers: 3239

Kudos [?]: 22316 [0], given: 2613

Re: What is the greatest prime factor of [#permalink] New post 12 Nov 2012, 11:10
Expert's post
dbiersdo wrote:
thevenus wrote:

=(2)^34-(2)^28
=(2)^28{(2)^6-1}


I don't get the transition here... what's the process involved that these two equal one another??


4^{17}-2^{28}=2^{34}-2^{28} --> factor out 2^28: 2^{34}-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7 --> the greatest prime factor is 7.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2315
Followers: 241

Kudos [?]: 2054 [0], given: 677

Re: What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 12 Nov 2012, 16:37
Expert's post
Great explanation Mod :)

Those questions seems simple when you master the concepts but indeed are really tough :)

@ vandygrad11

Quote:
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.

when you master the concept and you know them cold..........In my opinion the only way is to practice questions from all level to see different things from odds angles

;)
_________________

COLLECTION OF QUESTIONS
Quant: 1. Bunuel Signature Collection - The Next Generation 2. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 3. Veritas Prep Blog PDF Version
Verbal:1. Best EXTERNAL resources to tackle the GMAT Verbal Section 2. e-GMAT's ALL CR topics-Consolidated 3. New Critical Reasoning question bank by carcass 4. Meaning/Clarity SC Question Bank by Carcass_Souvik 5. e-GMAT's ALL SC topics-Consolidated-2nd Edition 6. The best reading to improve Reading Comprehension

TOEFL iBT
Best resources to tackle each section of the TOEFL iBT

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1723
Followers: 165

Kudos [?]: 33 [0], given: 0

Premium Member
Re: What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 03 Dec 2013, 07:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 649
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 146 [0], given: 161

Re: What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 26 Feb 2014, 00:39
4^17 - 2^28 =
4^17 - 4^14 =
4^14 . (4^3 - 1) =

4^14 . 63 = 4^14. 9. 7

Answer = 7 = D
_________________

Kindly press "Kudos" to appreciate

Manager
Manager
avatar
Joined: 05 Jun 2012
Posts: 72
Schools: IIMA
Followers: 0

Kudos [?]: 1 [0], given: 55

Re: What is the greatest prime factor of 4^17 - 2^28? [#permalink] New post 01 Jul 2014, 05:40
4 is not prime, so break the 4's down into 2's:
4^17 = (2^2)^17 = 2^34
so we have
2^34 - 2^28
at this point, make a common exponent, so that we can factor out the largest possible common factor.
(2^28)(2^6) - (2^28)
(2^28)(2^6 - 1)
(2^28)(63)
finish breaking into primes:
(2^28)(3)(3)(7)
so the greatest prime factor is 7 :)
_________________

If you are not over prepared then you are under prepared !!!

Re: What is the greatest prime factor of 4^17 - 2^28?   [#permalink] 01 Jul 2014, 05:40
    Similar topics Author Replies Last post
Similar
Topics:
What is the greatest prime factor of (4^17) - (2^28)? a. 2 kuristar 5 11 Jun 2006, 16:16
What is the greatest prime factor of 4^17 - 2^28 Matador 4 17 Apr 2006, 15:50
What is the greatest prime factor of 4^17 - 2^28 ? I tobiastt 2 25 Nov 2005, 08:41
What is the greatest prime factor of 4^17 -2^28? (A) 2 kimmyg 4 10 Oct 2005, 11:20
What is the greatest prime factor of 4^17 - 2^28 zoom 12 10 Sep 2005, 12:08
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.