Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Oct 2010
Posts: 38
WE 1: 3 yrs

What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
13 Nov 2010, 10:55
Question Stats:
66% (00:35) correct 34% (00:36) wrong based on 1954 sessions
HideShow timer Statistics
What is the greatest prime factor of 4^17  2^28? A. 2 B. 3 C. 5 D. 7 E. 11
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47084

Re: Factors [#permalink]
Show Tags
13 Nov 2010, 11:03




Manager
Status: Planning to retake.
Affiliations: Alpha Psi Omega
Joined: 25 Oct 2010
Posts: 86
Concentration: General Management, Entrepreneurship
GPA: 3.16

Re: Factors [#permalink]
Show Tags
13 Nov 2010, 12:40
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



Math Expert
Joined: 02 Sep 2009
Posts: 47084

Re: Factors [#permalink]
Show Tags
13 Nov 2010, 12:47



Manager
Status: Planning to retake.
Affiliations: Alpha Psi Omega
Joined: 25 Oct 2010
Posts: 86
Concentration: General Management, Entrepreneurship
GPA: 3.16

Re: Factors [#permalink]
Show Tags
13 Nov 2010, 13:05
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



Math Expert
Joined: 02 Sep 2009
Posts: 47084

Re: Factors [#permalink]
Show Tags
13 Nov 2010, 13:10



Manager
Joined: 08 Jun 2010
Posts: 123

Re: Factors [#permalink]
Show Tags
17 Jan 2011, 10:01
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



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4667

Re: what is the greatest prime factor? [#permalink]
Show Tags
05 Jun 2012, 15:22
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/gmatmathfactors/Does all that make sense? Please let me know if you have any further questions. Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Current Student
Joined: 08 Jan 2009
Posts: 309

Re: what is the greatest prime factor? [#permalink]
Show Tags
05 Jun 2012, 15:24
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



Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 126
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)

Re: what is the greatest prime factor? [#permalink]
Show Tags
05 Jun 2012, 18:58
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(641) = 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



Senior Manager
Joined: 13 Jan 2012
Posts: 290
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)

Re: what is the greatest prime factor? [#permalink]
Show Tags
06 Jun 2012, 00:41
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/gmatmathfactors/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.



Senior Manager
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 490
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

What is the greatest prime factor of [#permalink]
Show Tags
30 Aug 2012, 11:46
Let's simplify (4)^172^28 ={(2)^2}^17(2)^28 =(2)^34(2)^28 =(2)^28{(2)^61} =(2)^28{641} =(2)^28{63} =(2)^28{3x3x 7} clearly 7
_________________
" Make more efforts " Press Kudos if you liked my post



Senior Manager
Joined: 03 Sep 2012
Posts: 387
Location: United States
Concentration: Healthcare, Strategy
GPA: 3.88
WE: Medicine and Health (Health Care)

Re: What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
01 Oct 2012, 06:03
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



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1264
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: What is the greatest prime factor of 4^17  2^28 [#permalink]
Show Tags
12 Nov 2012, 08:30
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 2^342^28. Take 2^28 as common. 2^28(2^61) It will become, 2^28 * (641) 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 ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Intern
Joined: 03 Aug 2012
Posts: 20
Location: United States (OR)
Concentration: Finance, International Business
GPA: 3.53
WE: Analyst (Entertainment and Sports)

Re: What is the greatest prime factor of [#permalink]
Show Tags
12 Nov 2012, 12:04
thevenus wrote: =(2)^34(2)^28 =(2)^28{(2)^61}
I don't get the transition here... what's the process involved that these two equal one another??



Math Expert
Joined: 02 Sep 2009
Posts: 47084

Re: What is the greatest prime factor of [#permalink]
Show Tags
12 Nov 2012, 12:10



Board of Directors
Joined: 01 Sep 2010
Posts: 3436

Re: What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
12 Nov 2012, 17:37
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 AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
26 Feb 2014, 01:39
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 "+1 Kudos" to appreciate



Manager
Joined: 05 Jun 2012
Posts: 89

Re: What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
01 Jul 2014, 06:40
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 !!!



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646

Re: What is the greatest prime factor of 4^17  2^28? [#permalink]
Show Tags
14 Mar 2016, 08:21




Re: What is the greatest prime factor of 4^17  2^28?
[#permalink]
14 Mar 2016, 08:21



Go to page
1 2
Next
[ 30 posts ]



