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 →

Arithmetic

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members
Thanked: 331 times

by cramya » Thu Mar 12, 2009 2:49 pm
Basically its asking how many factors does 130 have?

The easy way to do it would be to break down 130 in to its prime factors first

130 =2*5*13 = 2^1*5^1*13^1


Now to find the number of factors add 1 to the exponent of each prime factor and multiply

(1+1) (1+1) (1+1) = 8 unique factors


Illustarting with another eg:

For 12 = 2*3*2 = 2^2 * 3^1

No of factors would be (2+1) (1+1) = 6

12 has 6 unique factors


Hope this helps!

Regards,
CR
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Wed Mar 11, 2009 9:56 pm
Location: Whitler, BC, Canada

by franciskyle » Thu Mar 12, 2009 2:52 pm
To do this quicker, you could have looked at the numerator. Since it ends in 0, you automatically know that it is divisible by 1,2,5,10. That gives us 4 factors, which need each some other unique factor to multiply with to get 130 - therefore you immediately know that there are AT LEAST 8 factors. Since 8 is the highest option, you can quickly select it.
Last edited by franciskyle on Thu Mar 12, 2009 2:55 pm, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 73
Joined: Wed Jan 28, 2009 9:00 am
Thanked: 6 times
GMAT Score:680

by Alara533 » Thu Mar 12, 2009 2:53 pm
Is the answer 8?

Approach-

For 130/x to be an integer, x must be a factor of 130

Find prime factors of 130 -> 2,5,13 --> 3 factors
The multiples of these factors will also be factors of 130, ie
5 x 2 = 10
5 x 13 = 65
2 x 13 = 26
5 x 2 x 13 = 130

and finally 1 is also a factor of 130...so total 8 possible values for x
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Sat Dec 13, 2008 9:00 am

by lolo » Thu Mar 12, 2009 3:04 pm
Thank you guys for these great explanations.

Do you have other ways to find the OA : 8 ?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Wed Mar 11, 2009 9:56 pm
Location: Whitler, BC, Canada

by franciskyle » Thu Mar 12, 2009 7:22 pm
Hi cramya...

I find the way you solved this problem interesting.
cramya wrote:
The easy way to do it would be to break down 130 in to its prime factors first

130 =2*5*13 = 2^1*5^1*13^1


Now to find the number of factors add 1 to the exponent of each prime factor and multiply

(1+1) (1+1) (1+1) = 8 unique factors
Are you able to explain the theory behind your answer? Why should I expect that when I add 1 to each exponent of the prime factors and then multiply them I will arrive at the total number of factors?

I'm sorry if this is silly, but I am having trouble piecing this logic.

Thanks :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members
Thanked: 331 times

by cramya » Thu Mar 12, 2009 8:00 pm
Frankie,
Giving credit to the source:

https://www.gmathacks.com/gmat-math/numb ... teger.html

Hope this helps!

Regards,
CR
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1