upon factorization we get 2^28*(2^6 - 1) = 2^28*63, hence the greatest prime factor of that is 7.
Cheers
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
What is the greatest prime factor
Source: Beat The GMAT — Problem Solving |
-
indiantiger
- Master | Next Rank: 500 Posts
- Posts: 362
- Thanked: 26 times
given to us 4^17 - 2^28 and need to find its Greatest prime factor
when you see this question the first thing is to make the bases same
=(2^2)^17 - 2^28
=2^34 - 2^28
now we have same bases so we can take out 2^28
=2^28(2^6 - 1)
=2^28(64 -1)
=2^28*63
=2^28 * 7 * 3 * 3
from here you can see the greatest prime factor is 7 (answer option D)
when you see this question the first thing is to make the bases same
=(2^2)^17 - 2^28
=2^34 - 2^28
now we have same bases so we can take out 2^28
=2^28(2^6 - 1)
=2^28(64 -1)
=2^28*63
=2^28 * 7 * 3 * 3
from here you can see the greatest prime factor is 7 (answer option D)
"Single Malt is better than Blended"
Hi guys:
Can u believe that I wrote the -1, but I didn't use it??
When i try to do things against time, I do foolish errors like this.
Thanks for your time.
Silvia
Can u believe that I wrote the -1, but I didn't use it??
When i try to do things against time, I do foolish errors like this.
Thanks for your time.
Silvia
-
Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Thanked: 335 times
Silvia, I can definitely believe it. I make this type of error too often.
In general, when solving questions about factors, divisibility or primes, it's a good idea to transform your numbers into their prime factors. In this case, 4^17 - 2^28 becomes 2^34 - 2^28.
To find the factors of an expression, factor it. in this case, you can factor out 2^28 from both sides to get 2^28 (2^6 - 1). The only prime factor of the portion outside the parenthesis is 2. The portion inside the parentheses simplifies to 63. It's greatest prime factor is 7. Thus the greatest prime factor of the initial expression is 7. The correct answer is D.
For more detailed explanation and a video solution, have a look at GMATPrep question 1121. If you struggle with similar questions, set topic to 'Exponents & Roots' and difficulty to '600-700 AND 700+' when you use the drill generator.
Good luck,
-Patrick
In general, when solving questions about factors, divisibility or primes, it's a good idea to transform your numbers into their prime factors. In this case, 4^17 - 2^28 becomes 2^34 - 2^28.
To find the factors of an expression, factor it. in this case, you can factor out 2^28 from both sides to get 2^28 (2^6 - 1). The only prime factor of the portion outside the parenthesis is 2. The portion inside the parentheses simplifies to 63. It's greatest prime factor is 7. Thus the greatest prime factor of the initial expression is 7. The correct answer is D.
For more detailed explanation and a video solution, have a look at GMATPrep question 1121. If you struggle with similar questions, set topic to 'Exponents & Roots' and difficulty to '600-700 AND 700+' when you use the drill generator.
Good luck,
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
Patrick_GMATFix wrote:Silvia, I can definitely believe it. I make this type of error too often.
For more detailed explanation and a video solution, have a look at GMATPrep question 1121.
Can't login.
Please sign in or register to access this resource
after registering it says it is paid
-
Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Thanked: 335 times
Send me a PM and I'll help you get free access. Or just request the free license that's offered as an alternative
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
