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

 It is currently 02 Jul 2015, 15:40

### 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
TAGS:
Manager
Joined: 05 Nov 2005
Posts: 232
Location: Germany
Followers: 2

Kudos [?]: 18 [0], given: 0

Prime factor [#permalink]  20 Dec 2005, 07:59
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: 285
Followers: 1

Kudos [?]: 2 [0], given: 0

4^14(4^3-1)

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

D
Manager
Joined: 05 Nov 2005
Posts: 232
Location: Germany
Followers: 2

Kudos [?]: 18 [0], given: 0

I am not that fast, can you eludcidate please?
Director
Joined: 17 Dec 2005
Posts: 548
Location: Germany
Followers: 1

Kudos [?]: 15 [0], given: 0

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: 5240
Followers: 23

Kudos [?]: 191 [0], given: 0

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
Followers: 1

Kudos [?]: 2 [0], given: 0

Good job old dream... I agree w/ 7
VP
Joined: 06 Jun 2004
Posts: 1059
Location: CA
Followers: 2

Kudos [?]: 54 [0], given: 0

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: 397
Location: Chicago, IL
Followers: 3

Kudos [?]: 29 [0], given: 17

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: 1813
Followers: 4

Kudos [?]: 56 [0], given: 0

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: 5068
Location: Singapore
Followers: 23

Kudos [?]: 193 [0], given: 0

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: 14 Apr 2005
Posts: 418
Location: India, Chennai
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: Prime factor [#permalink]  23 Dec 2005, 00:46
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, 00:46
Similar topics Replies Last post
Similar
Topics:
1 Factors and Prime Factors 1 30 Jan 2014, 09:34
2 Prime factorization 4 20 Oct 2012, 11:11
Prime Factorization 6 10 Mar 2011, 03:51
1 Prime Factors 1 12 Apr 2009, 07:59
1 Prime factors 2 18 Nov 2008, 08:46
Display posts from previous: Sort by