Last visit was: 19 Nov 2025, 22:25 It is currently 19 Nov 2025, 22:25
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
IgnitedMind
User avatar
Joined: 28 Aug 2008
Last visit: 10 Mar 2009
Posts: 53
Own Kudos:
217
 [43]
Posts: 53
Kudos: 217
 [43]
What is the greatest prime factor of 2^100 - 2^96? 11 Sep 2008, 14:11
4
Kudos
Add Kudos
39
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

76% (00:47) correct 24% (01:01) wrong based on 918 sessions

History

Date
Time
Result
Not Attempted Yet
What is the greatest prime factor of 2^100 - 2^96?

A. 2
B. 3
C. 5
D. 7
E. 11
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,395
 [11]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,395
 [11]
What is the greatest prime factor of 2^100 - 2^96? 21 Jan 2013, 10:47
6
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
ebliss
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?

Thanks!
Show more

Sure.

What is the greatest prime factor of 2^100 - 2^96?

A. 2
B. 3
C. 5
D. 7
E. 11

    \(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\).

Now, factor out 2^{96}:

    \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\).


The greatest prime factor is 5.

Answer: C.

Hope it's clear.
General Discussion
User avatar
x2suresh
User avatar
Joined: 07 Nov 2007
Last visit: 18 Aug 2012
Posts: 715
Own Kudos:
3,139
 [3]
Given Kudos: 5
Location: New York
Posts: 715
Kudos: 3,139
 [3]
What is the greatest prime factor of 2^100 - 2^96? 11 Sep 2008, 14:28
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
IgnitedMind
What is the greatest prime factor of 2^100 - 2^96?

A. 2

B. 3

C. 5

D. 7

E. 11
Show more

2^100 - 2^96 = 2^4*2^96 -2^96
= 2^96 (16-1) = 2^96 *5*3

5 is the greatest factor
C
User avatar
ssandeepan
User avatar
Joined: 09 Jul 2007
Last visit: 13 Jun 2010
Posts: 116
Own Kudos:
1,740
 [2]
Posts: 116
Kudos: 1,740
 [2]
What is the greatest prime factor of 2^100 - 2^96? 11 Sep 2008, 17:25
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
2^100 - 2^96=2^96 ( 2^4-1)=2^96*3*5

so greatest prime factor =5
avatar
ebliss
avatar
Joined: 14 Jul 2012
Last visit: 01 Nov 2016
Posts: 1
Given Kudos: 3
Posts: 1
Kudos: 0
What is the greatest prime factor of 2^100 - 2^96? 21 Jan 2013, 10:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?

Thanks!
User avatar
chiccufrazer1
User avatar
Joined: 04 Jan 2013
Last visit: 10 Dec 2013
Posts: 64
Own Kudos:
75
Given Kudos: 1
Posts: 64
Kudos: 75
What is the greatest prime factor of 2^100 - 2^96? 21 Jan 2013, 11:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
ebliss
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?

Thanks!

Sure.

What is the greatest prime factor of 2^100 - 2^96?

A. 2
B. 3
C. 5
D. 7
E. 11

\(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\).

Now, factor out 2^{96}: \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\). The greatest prime factor is 5.

Answer: C.

Hope it's clear.
Show more

@bunuel..2^96-2^96=2^1 according to index laws..in our factorised equation 2^4*2^96-2^96 the answer is 16*2=32..can we do prime factorisation on 32 where by k/2 +k/3 +k/5--->32/2+32/3+32/5?would we just take the 5 as our largest factor?but we know 5 is not a factor of 32..where am i missing the details please tell me..thanks in advance :)

Posted from my mobile device
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,395
 [2]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,395
 [2]
What is the greatest prime factor of 2^100 - 2^96? 21 Jan 2013, 11:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chiccufrazer1
Bunuel
ebliss
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?

Thanks!

Sure.

What is the greatest prime factor of 2^100 - 2^96?

A. 2
B. 3
C. 5
D. 7
E. 11

\(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\).

Now, factor out 2^{96}: \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\). The greatest prime factor is 5.

Answer: C.

Hope it's clear.

@bunuel..2^96-2^96=2^1 according to index laws..in our factorised equation 2^4*2^96-2^96 the answer is 16*2=32..can we do prime factorisation on 32 where by k/2 +k/3 +k/5--->32/2+32/3+32/5?would we just take the 5 as our largest factor?but we know 5 is not a factor of 32..where am i missing the details please tell me..thanks in advance :)

Posted from my mobile device
Show more

Not sure I understand your post.

First of all, 2^96-2^96=0 not 2.

Next, \(2^4*2^{96}-2^{96}\) equals to \(2^{96}*3*5\) not 32.
User avatar
dakshita1234
User avatar
Joined: 15 Jan 2024
Last visit: 14 Jun 2024
Posts: 8
Own Kudos:
3
Given Kudos: 2
Posts: 8
Kudos: 3
What is the greatest prime factor of 2^100 - 2^96? 13 Feb 2024, 16:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Hi
Can we use the concept of cyclicity in this? 

2^100 will have units digit as 4
and so will 2^96
Subtracting, 4-4 = 0
So 0 is the units place of the difference 
Thus, out ouf all the options, 5 fits the best 

Please let me know­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,590
Own Kudos:
1,079
Posts: 38,590
Kudos: 1,079
What is the greatest prime factor of 2^100 - 2^96? 18 May 2025, 00:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts