It is currently 24 Jun 2017, 08:50

### 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 June
Open Detailed Calendar

# Exponents / prime factors question

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 06 Oct 2007
Posts: 6
Exponents / prime factors question [#permalink]

### Show Tags

07 Oct 2007, 17:43
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

a) 2
b) 3
c) 5
d) 7
e) 11

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie
Manager
Joined: 10 Jan 2005
Posts: 63

### Show Tags

07 Oct 2007, 18:00
HEHE. I just took the GMATPrep 2 and got this problem wrong. Why did I get it wrong? Simple, careless mistake with the exponent rule: x^y * x^z = x ^(y+z)

But this question has a subtraction so that rule does not apply. If you did what I did, you would choose 2 as the answer. As soon as I saw my careless mistake, I knew how to get the correct answer

4^17 = (2^2)^17 = 2^34

2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 (64-1) = 2^28 * 63

2^28 has 2 as the highest prime factor
63 = 7*9 = 7*3*3 so 7 is the highest prime factor. Answer is 7 D.
Director
Joined: 22 Aug 2007
Posts: 566
Re: Exponents / prime factors question [#permalink]

### Show Tags

07 Oct 2007, 19:14
jthong wrote:
This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

a) 2
b) 3
c) 5
d) 7
e) 11

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie

also D,

same reasoning as of mayonnai5e.
Intern
Joined: 06 Oct 2007
Posts: 6
Exponents / prime factors question [#permalink]

### Show Tags

07 Oct 2007, 19:19
Thanks! I'm still not getting the bit about 64-1... Can you explain a bit more?
Director
Joined: 22 Aug 2007
Posts: 566
Re: Exponents / prime factors question [#permalink]

### Show Tags

07 Oct 2007, 22:57
jthong wrote:
Thanks! I'm still not getting the bit about 64-1... Can you explain a bit more?

2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 x (64-1) = 2^28 * 63

Make prime factorization for 63:

3 x 3 x 7 = 63,

so 2^34 - 2^28= 2^28 x 3 x 3 x 7

among prime factors: 2, 3, 7. Seven is the biggest.

Manager
Joined: 28 Sep 2007
Posts: 210

### Show Tags

08 Oct 2007, 07:38
not sure how you got 2^6-1 from 2^28?
CEO
Joined: 29 Mar 2007
Posts: 2559
Re: Exponents / prime factors question [#permalink]

### Show Tags

08 Oct 2007, 11:50
jthong wrote:
This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

a) 2
b) 3
c) 5
d) 7
e) 11

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie

4^17 can be rewritten as (2^2)^17 ---> 2^34

So we now have 2^34-2^28. Factor---> 2^28(2^6-1) U should at least know that 2^5=32, itd just be helpful for the GMAT.

So 2^6 is equals 64. 64-1=63. Greatest prime factor of 63 is 7. (7*9)

So ans is D.
CEO
Joined: 29 Mar 2007
Posts: 2559

### Show Tags

08 Oct 2007, 11:53
jingy77 wrote:
not sure how you got 2^6-1 from 2^28?

2^28(2^6-1) ---> is the same as 2^28*2^6 -2^28---> 2^34-2^28

When multiplying numbers w/ same base we add exponents.

Ex/ x^2*x^3=x^5 ---> 2+3=5.

Same with this here. 28+6=34.
08 Oct 2007, 11:53
Display posts from previous: Sort by

# Exponents / prime factors question

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.