BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
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
Start Free 5-Day Trial Read 559 Reviews →

What is the greatest prime factor of 1+2+3+ . . . + 40?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members
by Gmat_mission » Sun May 13, 2018 10:15 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

What is the greatest prime factor of 1 + 2 + 3 + . . . + 40?

A. 17
B. 29
C. 31
D. 37
E. 41

[spoiler]OA=E[/spoiler].

What is the fastest way to solve this PS question? Could someone explain this question to me? Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times

by Vincen » Sun May 13, 2018 10:52 am
Gmat_mission wrote:What is the greatest prime factor of 1 + 2 + 3 + . . . + 40?

A. 17
B. 29
C. 31
D. 37
E. 41

[spoiler]OA=E[/spoiler].

What is the fastest way to solve this PS question? Could someone explain this question to me? Thanks.
Hello Gmat_mission.

Here, a useful tool that we can use is that the sum of the first n positive integers is equal to n*(n+1)/2.

Therefore, here we have: $$1+2+3+\cdots+40=\frac{40\cdot\left(40+1\right)}{2}=\frac{40\cdot41}{2}=20\cdot41=2\cdot10\cdot41=2^2\cdot5\cdot41.$$ This shows that the greatest prime factor of the given sum is 41.

Hence, the correct answer is the option E.

I hope it helps.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sun May 13, 2018 11:24 am
Hi Vincen,

We're asked for the greatest prime factor of 1 + 2 + 3 + . . . + 40. This question has a number of built-in 'shortcuts' that you can use to avoid doing lots of calculations.

To start, the answers are all prime numbers - so we know that one of those numbers IS the greatest prime factor of that sum. Second, since we're dealing with 40 consecutive integers, we can use 'bunching' to spot a pattern:
1 + 40 = 41
2 + 39 = 41
3 + 38 = 41
Etc.

Since there are 40 terms, there will be 20 "pairs" of 41. By extension, 41 will divide evenly into that sum - and since it's the biggest prime number in the answer choices, it must be the answer.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Wed May 16, 2018 10:11 am
Gmat_mission wrote:What is the greatest prime factor of 1 + 2 + 3 + . . . + 40?

A. 17
B. 29
C. 31
D. 37
E. 41
The average of the consecutive integers from 1 to 40 inclusive is 41/2 and the number of integers is 40, so the sum is 40 x 41/2 = 20 x 41.

Thus, we see that the largest prime factor is 41.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1