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 →

Factors!

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 407
Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members
Thanked: 25 times
by Ozlemg » Fri Jul 15, 2011 3:09 am
How many distinct integers are factors of 90?

(A) 6
(B) 8
(C) 9
(D) 10
(E) 12

I know how to solve it; but want to learn whether there is an quick way to calculate if the number is high, such as 7654.

OA : E
Tnx
The more you suffer before the test, the less you will do so in the test! :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Fri Jul 15, 2011 3:48 am
Ozlemg wrote:How many distinct integers are factors of 90?...

I know how to solve it; but want to learn whether there is an quick way to calculate if the number is high, such as 7654
To find the number of distinct factors of an integer N, we have to first express the integer as the product of prime integers like N = (p^a)*(q^b)...

Then the number of distinct factors of integer N is (a + 1)(b + 1)...

Here, 90 = (2^1)*(3^2)*(5^1)
Hence, number of distinct integers of 90 is (1 + 1)*(2 + 1)*(1 + 1) = 2*3*2 = 12

If the number is 7654, then 7654 = 2*43*89
Hence, number of distinct integers of 7654 is (1 + 1)*(1 + 1)*(1 + 1) = 2*2*2 = 8
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Fri Jul 15, 2011 3:49 am
your posted q. ==> perform prime factorization of 90
90(2)45
45(3)15
15(3)5
5(5)1 ==> (2^1)*(3^2)*(5^1), the number of distinct factors will be (1+1)*(2+1)*(1+1) by adding 1 to the power of each prime factor, there will be 12 distinct factors

the same solution way should be applied to 7654

7654(2)3827
3827(43)89
89(89)1

(2^1)*(43^1)*(89^1) ==> (1+1)*(1+1)*(1+1)=8, so 8 distinct factors

use this link for prime factorization of big numbers https://www.math.wustl.edu/cgi-bin/primes
Ozlemg wrote:How many distinct integers are factors of 90?

(A) 6
(B) 8
(C) 9
(D) 10
(E) 12

I know how to solve it; but want to learn whether there is an quick way to calculate if the number is high, such as 7654.

OA : E
Tnx
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1