Last visit was: 22 Apr 2026, 22:36 It is currently 22 Apr 2026, 22:36
Home
Messages
Tests
Schools
Events
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
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,231
Own Kudos:
3,643
 [7]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,231
Kudos: 3,643
 [7]
What is the greatest prime factor of 49^19 - 7^35 03 Jan 2017, 11:40
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

63% (01:36) correct 37% (01:30) wrong based on 345 sessions

History

Date
Time
Result
Not Attempted Yet
What is the greatest prime factor of \(49^{19}-7^{35}\)

A) 2
B) 3
C) 7
D) 13
E) 19
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
vitaliyGMAT
User avatar
Joined: 13 Oct 2016
Last visit: 26 Jul 2017
Posts: 297
Own Kudos:
895
 [5]
Given Kudos: 40
GPA: 3.98
Posts: 297
Kudos: 895
 [5]
What is the greatest prime factor of 49^19 - 7^35 03 Jan 2017, 13:07
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
stonecold
What is the greatest prime factor of \(49^{19}-7^{35}\)
A)2
B)3
C)7
D)13
E)19
Show more

\((7^2)^{19} - 7^{35} = 7^{38} - 7^{35} = 7^{35}(7^3 - 1) = 7^{35}*342 = 7^{35}*2*3^2*19\)

Answer E
General Discussion
User avatar
Gmatprep550
User avatar
Joined: 21 Jul 2018
Last visit: 08 Nov 2019
Posts: 137
Own Kudos:
73
Given Kudos: 186
Products:
My Reviews
Posts: 137
Kudos: 73
What is the greatest prime factor of 49^19 - 7^35 27 Jan 2019, 22:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the greatest prime factor of 49^19−7^35

A) 2
B) 3
C) 7
D) 13
E) 19
User avatar
KanishkM
User avatar
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
Own Kudos:
512
 [1]
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Schools: DeGroote'21 Desautels '21 NUS '21
Posts: 755
Kudos: 512
 [1]
What is the greatest prime factor of 49^19 - 7^35 27 Jan 2019, 22:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Gmatprep550
What is the greatest prime factor of 49^19−7^35

A)2
B)3
C)7
D)13
E)19

I am not able to understand solution for this, can any one help
Show more

Would like to share my thoughts on this

\(49^{19}−7^{35}\)

Always reduce the terms in their lowest factors, said that

\(7^{2* 19} - 7^{35}\)

\(7^{35} ( 7^3 - 1)\)

\(7^{35}\), will always have 7 has a factor

\(7^3 - 1\), can be reduced to 342, which can be written as \(2 * 3^2 * 19\)

So out of this bunch 2,3,7 and 19

E is the largest prime number
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,696
Given Kudos: 105,850
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: 109,763
Kudos: 810,696
What is the greatest prime factor of 49^19 - 7^35 27 Jan 2019, 23:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Gmatprep550
What is the greatest prime factor of 49^19−7^35

A) 2
B) 3
C) 7
D) 13
E) 19
Show more

Merging topics.

Please do not re-post existing questions. Also, do not re-post questions from here: https://gmatclub.com/forum/stonecold-s- ... 17160.html Thank you.
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 22 Apr 2026
Posts: 8,627
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,627
Kudos: 5,190
What is the greatest prime factor of 49^19 - 7^35 28 Jan 2019, 02:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
What is the greatest prime factor of \(49^{19}-7^{35}\)

A) 2
B) 3
C) 7
D) 13
E) 19
Show more


\(49^{19}-7^{35}\)

7^35( 7^3-1)
7^35* 342
342= 2*3^2*19^1

so greatest prime factor
7^35 * 2*3^2*19^1

IMO E 19
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,447
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,447
What is the greatest prime factor of 49^19 - 7^35 22 Nov 2019, 17:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
What is the greatest prime factor of \(49^{19}-7^{35}\)

A) 2
B) 3
C) 7
D) 13
E) 19
Show more

49^19 - 7^35 = (7^2)^19 - 7^35
= 7^38 - 7^35
= (7^35)(7^3 - 1)
= (7^35)(343 - 1)
= (7^35)(342)
= (7^35)(2)(3)(3)(19)

Answer: E

Cheers,
Brent
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,963
Own Kudos:
1,117
Posts: 38,963
Kudos: 1,117
What is the greatest prime factor of 49^19 - 7^35 08 Apr 2025, 15:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts