It is currently 26 Jun 2017, 00:40

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

hcf of two no.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 18 Dec 2012
Posts: 2
hcf of two no. [#permalink]

Show Tags

New post 18 Dec 2012, 19:37
1
This post was
BOOKMARKED
If A = (2^(20) -1) and B = (2^(110) - 1). Then HCF(A,B) =
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1381
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: hcf of two no. [#permalink]

Show Tags

New post 18 Dec 2012, 20:29
Hii welcome to GMATCLUB.
Please see the rules before posting.

In this question, the answer must be 3.
Take two numbers for easy calculation: 2^6 and 2^8.
So 2^6 - 1=63, 2^8 - 1=255.
Hcf is 3.
Hence IMO for the two numbers in question, the hcf will be 3.
_________________

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

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
S
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India
Re: hcf of two no. [#permalink]

Show Tags

New post 19 Dec 2012, 00:27
2
This post received
KUDOS
Expert's post
juantheron wrote:
If A = (2^(20) -1) and B = (2^(110) - 1). Then HCF(A,B) =


Use a^2 - b^2 = (a + b)(a - b) to factorize the expressions.

\(A = 2^{20} - 1^{20} = 2^{10*2} - 1^{10*2} = (2^{10})^2 - (1^{10})^2 = (2^{10} + 1^{10})(2^{10} - 1^{10})\)
\(B = 2^{110} - 1^{110} = 2^{10*11} - 1^{10*11} = (2^{10})^{11} - (1^{10})^{11} = (2^{10} - 1^{10})(2^{100} + ....)\)

(Difference of odd powers is divisible by the difference of the numbers e.g. x^3 - y^3 is divisible by x-y)

The highest common factor must be\((2^{10} - 1^{10}) = 2^{10} - 1\)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1381
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: hcf of two no. [#permalink]

Show Tags

New post 19 Dec 2012, 02:57
Hi Karishma.
Is there any alternate way to do this question?
I tried picking up a smaller number but failed as evitable by your explanation.
_________________

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

Expert Post
Veritas Prep GMAT Instructor
User avatar
S
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India
Re: hcf of two no. [#permalink]

Show Tags

New post 19 Dec 2012, 21:02
Marcab wrote:
Hi Karishma.
Is there any alternate way to do this question?
I tried picking up a smaller number but failed as evitable by your explanation.


There is no reason that the HCF of two small numbers will be the same as the HCF of two larger numbers. The question is meant to test your application of algebraic identities.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Re: hcf of two no.   [#permalink] 19 Dec 2012, 21:02
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Two variables - two equations trap iliavko 5 16 Feb 2017, 08:58
10 Numbers Divisibility Tests, HCF and LCM NOTES kingb 3 14 Apr 2017, 01:30
3 Experts publish their posts in the topic HCF and LCM question apporach how to derive vidyakmr 3 31 Mar 2017, 07:19
5 Experts publish their posts in the topic Reverse of LCM / HCF rxs0005 12 30 May 2017, 23:42
1 Slope of two point Bigred2008 4 21 Mar 2011, 06:39
Display posts from previous: Sort by

hcf of two no.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| 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®.