GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Dec 2018, 07:51

TODAY:

MIT Sloan R1 Decisions - Join MIT Chat for Live Updates | Chat with UCLA Anderson Adcom @9am PT | Chat with Yale SOM R1 Admit 10am PT

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

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

What is the greatest prime factor of 8^12 - 2^30?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51307
What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

25 May 2016, 03:24
1
12
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:08) correct 35% (01:21) wrong based on 320 sessions

HideShow timer Statistics

What is the greatest prime factor of 8^12 - 2^30?

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

_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2130
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

25 May 2016, 03:32
4
2
8^12 - 2^30
=(2^3)^12 - 2^30
= 2^36 - 2^30
= 2^30 (2^6 -1)
= 2^30 * (64-1)
= 2^30 * 63
= 2^30 * 9 *7
= 2^30 * 3^2 * 7
greatest prime factor is 7
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

General Discussion
Moderator
Joined: 21 Jun 2014
Posts: 1104
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

25 May 2016, 07:50
1
Bunuel wrote:
What is the greatest prime factor of 8^12 - 2^30?

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

8^12 - 2^30?

8 = 2^3
8^12 = 2^36

2^36 - 2^30 = 2^30 (2^6 - 1) = 2^30 (64 - 1) = 2^30 (63) = 2^30 (7*3*3)

hence 2,3,7 are the prime factors of 8^12 - 2^30. here, 7 is the greatest prime factor.

Option D is correct.
_________________

---------------------------------------------------------------
Target - 720-740
Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1356
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

29 Dec 2016, 09:59
1
Bunuel wrote:
What is the greatest prime factor of 8^12 - 2^30?

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

My take:

$$8$$$$^{12}$$$$-$$$$2^{30}$$

$$2$$$$^{3*12}$$ $$- 2$$$$^{30}$$

$$2^{36}$$ $$- 2^{30}$$

$$2^{30} (2^6-1)$$

$$2^{30} * 63$$

$$2^{30}*3*3*7$$

Hence "7" is the GREATEST prime (D)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Director
Joined: 12 Nov 2016
Posts: 732
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

10 Apr 2017, 18:29
Bunuel wrote:
What is the greatest prime factor of 8^12 - 2^30?

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

In order to solve this question we need to factor out the set of exponents until we find a prime number.

8^12-2^30
4^24-2^30
(2^24)( 2^12)-2^30
2^36-2^30
2^30-(2^6-1)
2^30-(64-1)
2^30-(63)

prime factorization of 63

(3)(3)(7)

Seven is the largest prime number and thus the answer
CEO
Joined: 11 Sep 2015
Posts: 3243
Re: What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

21 Feb 2018, 07:52
1
Top Contributor
Bunuel wrote:
What is the greatest prime factor of 8^12 - 2^30?

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

To determine the greatest prime factor of 8^12 - 2^30, we must find the prime factorization of 8^12 - 2^30

Given: 8^12 - 2^30
Rewrite 8 as to get: ()^12 - 2^30
Apply Power of Power rule to get: 2^36 - 2^30
Factor out 2^30 to get: 2^30(2^6 - 1)
Evaluate: 2^30(64- 1)
Simplify: 2^30(63)
Factor 63 to get: (2^30)(3)(3)(7)

At this point, we can see that the greatest prime factor is 7

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: What is the greatest prime factor of 8^12 - 2^30?  [#permalink]

Show Tags

22 Feb 2018, 16:48
Bunuel wrote:
What is the greatest prime factor of 8^12 - 2^30?

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

We can simplify the given expression:

(2^3)^12 - 2^30

2^36 - 2^30

2^30(2^6 - 1) = 2^30(63) = 2^30 x 9 x 7 = 2^30 x 3^2 x 7

So the largest prime factor is 7.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: What is the greatest prime factor of 8^12 - 2^30? &nbs [#permalink] 22 Feb 2018, 16:48
Display posts from previous: Sort by