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

 It is currently 04 Jul 2015, 12:48

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Exponents / prime factors question

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 06 Oct 2007
Posts: 6
Followers: 0

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

Exponents / prime factors question [#permalink]  07 Oct 2007, 16:43
1
This post was
BOOKMARKED
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
Followers: 1

Kudos [?]: 4 [0], given: 0

[#permalink]  07 Oct 2007, 17:00
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: 569
Followers: 1

Kudos [?]: 16 [0], given: 0

Re: Exponents / prime factors question [#permalink]  07 Oct 2007, 18:14
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
Followers: 0

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

Exponents / prime factors question [#permalink]  07 Oct 2007, 18:19
Thanks! I'm still not getting the bit about 64-1... Can you explain a bit more?
Director
Joined: 22 Aug 2007
Posts: 569
Followers: 1

Kudos [?]: 16 [0], given: 0

Re: Exponents / prime factors question [#permalink]  07 Oct 2007, 21:57
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: 213
Followers: 1

Kudos [?]: 17 [0], given: 0

[#permalink]  08 Oct 2007, 06:38
not sure how you got 2^6-1 from 2^28?
CEO
Joined: 29 Mar 2007
Posts: 2585
Followers: 17

Kudos [?]: 244 [0], given: 0

Re: Exponents / prime factors question [#permalink]  08 Oct 2007, 10:50
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: 2585
Followers: 17

Kudos [?]: 244 [0], given: 0

[#permalink]  08 Oct 2007, 10:53
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.
[#permalink] 08 Oct 2007, 10:53
Similar topics Replies Last post
Similar
Topics:
1 Question Regarding Multiples, factors and primes! 6 09 Nov 2011, 15:11
Factoring Exponents 1 31 Jul 2010, 13:26
Basic Factoring Exponents Question 1 01 Nov 2008, 17:28
Prime factor questions 4 27 Jul 2007, 12:09
Prime factor 10 20 Dec 2005, 07:59
Display posts from previous: Sort by

# Exponents / prime factors question

 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®.