It is currently 26 Jun 2017, 19:41

### 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

# Prime factor

Author Message
Manager
Joined: 05 Nov 2005
Posts: 227
Location: Germany

### Show Tags

20 Dec 2005, 08:59
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How to solve this?

What is the greatest prime factor of 4^17 - 2^28 ?

(a) 2
(b) 3
(c) 5
(d) 7
(e) 11
Senior Manager
Joined: 09 Aug 2005
Posts: 283

### Show Tags

20 Dec 2005, 09:14
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

D
Manager
Joined: 05 Nov 2005
Posts: 227
Location: Germany

### Show Tags

20 Dec 2005, 09:21
I am not that fast, can you eludcidate please?
Director
Joined: 17 Dec 2005
Posts: 547
Location: Germany

### Show Tags

20 Dec 2005, 09:50
4^17 - 2^28 = 4^17 - 4^14 = 4^14 (4^3 - 1), thats the key

4^14 will have the smallest prime possibble 2, but

4^3 - 1 = 63 = 7*3*3, so the greatest prime is 7
Current Student
Joined: 29 Jan 2005
Posts: 5218

### Show Tags

20 Dec 2005, 10:00
old_dream_1976 wrote:
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

D

Nice.....
Senior Manager
Joined: 05 Oct 2005
Posts: 485

### Show Tags

20 Dec 2005, 11:02
Good job old dream... I agree w/ 7
VP
Joined: 06 Jun 2004
Posts: 1053
Location: CA

### Show Tags

20 Dec 2005, 12:50
Yup, agree with old dream's working. 7 it is
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Senior Manager
Joined: 03 Nov 2005
Posts: 384
Location: Chicago, IL

### Show Tags

20 Dec 2005, 13:58
4^17 - 2^28 ===>2^34*2^28

==>2^28(2^6-1)

==>2^28*64-1

==>2^28*7*3^2

D stands
_________________

Hard work is the main determinant of success

SVP
Joined: 16 Oct 2003
Posts: 1801

### Show Tags

20 Dec 2005, 19:55
2^28(2^6 - 1)
2^26*63
2^26*21*3
2^26*7*3*3
7 is the greatest prime factor.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

20 Dec 2005, 20:04
You will notice 4^17 = 2^34. So the question becomes 2^34 - 2^28 = 2^28(2^6-1) = 2^28(63)

The prime factors are 2^28 * 3 * 21 = 2^28 * 3 * 3 * 7

Greatest prime factor = 7
Senior Manager
Joined: 15 Apr 2005
Posts: 415
Location: India, Chennai

### Show Tags

23 Dec 2005, 01:46
sandalphon wrote:
How to solve this?

What is the greatest prime factor of 4^17 - 2^28 ?

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

= 2^34 - 2^28
= 2^28(2^6-1)
= 2^28 (64-1)
= 2^28 * 63
= 2 ^28 * 7 * 9
= 2^ 28 * 7 * 3^2
So 7 is the greatest prime factor.
Re: Prime factor   [#permalink] 23 Dec 2005, 01:46
Display posts from previous: Sort by