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

It is currently 21 Aug 2014, 20:04

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

hcf of two no.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 18 Dec 2012
Posts: 2
Followers: 0

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

hcf of two no. [#permalink] New post 18 Dec 2012, 18:37
1
This post was
BOOKMARKED
If A = (2^(20) -1) and B = (2^(110) - 1). Then HCF(A,B) =
Expert Post
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: 127

Kudos [?]: 590 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: hcf of two no. [#permalink] New post 18 Dec 2012, 19:29
Expert's post
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
Joined: 16 Oct 2010
Posts: 4668
Location: Pune, India
Followers: 1073

Kudos [?]: 4781 [2] , given: 163

Re: hcf of two no. [#permalink] New post 18 Dec 2012, 23:27
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
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: 127

Kudos [?]: 590 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: hcf of two no. [#permalink] New post 19 Dec 2012, 01:57
Expert's post
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
Joined: 16 Oct 2010
Posts: 4668
Location: Pune, India
Followers: 1073

Kudos [?]: 4781 [0], given: 163

Re: hcf of two no. [#permalink] New post 19 Dec 2012, 20:02
Expert's post
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: hcf of two no.   [#permalink] 19 Dec 2012, 20:02
    Similar topics Author Replies Last post
Similar
Topics:
HCF of two numbers is 23. Find the smaller of the two number cumulonimbus 4 07 May 2014, 21:28
7 Experts publish their posts in the topic If the LCM of two numbers a and b is 1104 and their HCF is 4 ricsingh 5 09 Apr 2014, 09:24
The sum of two numbers is 588 and their HCF is 49. How many salsal 0 06 Sep 2013, 13:11
5 Experts publish their posts in the topic The sum of two number is 588 and their HCF is 49. How many NYC5648 16 07 Jun 2012, 11:44
The sum of two numbers is 216 and thier HCF or GCD is 27 rxs0005 2 28 Dec 2004, 18:18
Display posts from previous: Sort by

hcf of two no.

  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®.