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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

How many positive factors?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members
Thanked: 335 times

by Patrick_GMATFix » Sun Mar 09, 2014 6:43 pm
The number of positive factors follows the formula below:

if x = m^a * n^b * o^c... where m, n and o are the distinct prime factors of x, then x must have (a+1)(b+1)(c+1)... positive factors.

The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).

Image

-Patrick
  • Ask me about tutoring.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sun Mar 09, 2014 5:50 pm
Thanked: 1 times

by vinaycfc » Sun Mar 09, 2014 6:57 pm
How many different positive integers are factors of 441?

A) 4
B) 6
C) 7
D) 9
E) 11


441=21^2

21=7*3

21^2=(7^2*3^2)

num of factors of a^n*b^m=(n+1)*(m+1)

num of factors of 7^2*7^3=(2+1)*(2+1)=3*3=9
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Sun Mar 09, 2014 6:57 pm
441 = 7 x 7 x 3 x 3 = (7)^2 * (3)^2

So factors = (2+1)(2+1) = 9
[spoiler]
{D}[/spoiler]
R A H U L
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] » Mon Mar 10, 2014 12:23 pm
Hi LulaBrazilia,

This type of question can be answered using a variety of approaches. Here's a method that uses Prime Factorization and a "list" of the options:

441 can be factored down in "any order"; if you can spot that it's 21x21, then great, but you can just factor it down one piece at a time...

441 = 3x147

147 = 3x49

49 = 7x7

So...
441 = 3x3x7x7

Now, let's list the factors. Every "combination" of those 4 numbers is required:
1 --->Don't forget this factor!!!! 1 is a factor of EVERYTHING
3
7
9 = 3x3
21 = 3x7
49 = 7x7
63 = 3x3x7
147 = 3x7x7
441 = 3x3x7x7

Total Factors: D

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 » Mon Mar 12, 2018 10:16 am
LulaBrazilia wrote:How many different positive integers are factors of 441?

A) 4
B) 6
C) 7
D) 9
E) 11
To determine the total number of positive factors, we first break 441 into its prime factors, add 1 to each exponent and multiply the results.

441 = 7^2 x 3^2

So the number of factors is (2 + 1)(2 + 1) = 3 x 3 = 9.

Answer: D

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