Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » GMAT Prep Math


 Page 1 of 1 [ 4 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

what is the greatest prime factor of 2^34-2^28

Author Message
chini
 Post subject: what is the greatest prime factor of 2^34-2^28
 Post Posted: Thu Jun 05, 2008 3:11 pm 
What is the greatest common factor of 2^34-2^28?

1) 2
2) 3
3) 5
4) 7
5) 11

I can't figure this out without doing out all of the math. Any pointers? Thanks
Top 
Success
 Post subject: Answer
 Post Posted: Thu Jun 05, 2008 3:45 pm 
(2^34-2^28)

if you pick out the common term
2^28 (2^6 - 1) = 2^28 ( 64-1)

2^28 (63 ) = take it term by term

2^28 has a prime number of 2.

63 / 3 = 21

21 / 3= 7

7 is a prime number, and thus, the highest.
I hope it is the answer............
And if it is not, could someone pls help us out.
Top 
chini
 Post subject:
 Post Posted: Thu Jun 05, 2008 9:59 pm 
Thanks for the help. 7 is the answer; however why do you reason that it is 2^28 (2^6-1)? Where does the 1 come from? Thanks.
Top 
rfernandez
 Post subject:
 Post Posted: Fri Jun 06, 2008 4:40 am 
Offline
ManhattanGMAT Staff


Posts: 386
Quote:
What is the greatest common factor of 2^34-2^28?

1) 2
2) 3
3) 5
4) 7
5) 11


Just to clarify, does the question actually read "What is the greatest prime factor...?" That's what I suspect. In order to find GCF, you need at least two numbers.



Quote:
Thanks for the help. 7 is the answer; however why do you reason that it is 2^28 (2^6-1)? Where does the 1 come from? Thanks.


The 1 comes from factoring out the common factor of 2^28. As an analogy, consider factoring x^8 - x^3. Here, the common factor is x^3. Pulling that out gives x^3(x^5 - 1). Similarly, 2^34 - 2^28 yields 2^28(2^6 - 1).
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 4 posts ] 





Who is online

Users browsing this forum: No registered users and 0 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: