• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

2,600 has how many positive divisors?

This topic has 5 expert replies and 0 member replies

2,600 has how many positive divisors?

Post
2,600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2666 messages
Followed by:
125 members
Upvotes:
1153
GMAT Score:
770
Post
VJesus12 wrote:
2,600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?
Neat shortcut for finding the number of divisors of a given value.

First, take the prime factorization of the number in question: 2600 = 26 * 100 = 2 * 13 * 2^2 * 5^2 = 2^3 * 5^2 * 13

Next, add one to the exponent of each prime base and multiply the results. (Note that 13 is the same as 13^1): (3+1)(2+1)(1+1) = (4)(3)(2) = 24. The answer is D

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post
Quote:
2,600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?
Hi VJesus12,
Let's take a look at your question.

We are asked to find the number of positive divisors of 2600.
In order to find number of positive divisors a number has, we find the prime factorization, and add one to all the exponents and multiply them.

Let's write 2600 as a product of its prime factors.
$$2600=\ 26\ \times100$$
$$2600=\ 2\times13\ \times10\times10$$
$$2600=\ 2\times13\ \times2\times5\times2\times5$$

2600 is now written as a product of its prime factors.
Let's now write the factors using exponents.
$$2600=\ 2^3\times5^2\times13^1$$

To find the number of positive divisors of 2600, add 1 to each exponent and multiply them.
$$=\left(3+1\right)\left(2+1\right)\left(1+1\right)$$
$$=\left(4\right)\left(3\right)\left(2\right)$$
$$=24$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

GMAT/MBA Expert

Post
VJesus12 wrote:
2,600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48
--------ASIDE------------------------------
IMPORTANT: If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
----ONTO THE QUESTION---------------------

2,600 has how many positive divisors?
2600 = (2^3)(5^2)(13^1)
So, the number of positive divisors of 2600 = (3+1)(2+1)(1+1)
=(4)(3)(2)
= 24
= D

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

GMAT Instructor Default Avatar
Joined
12 Sep 2012
Posted:
2635 messages
Followed by:
117 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post
If it's easier to see this visually, check out this great tutorial.

In the future, remember that Google is your friend! In a pinch you can usually find walkthroughs of most basic formulas such as this without having to wait a few hours for an expert to reply.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post
Here's a video that explains the rule AND explains why it works: https://www.gmatprepnow.com/module/gmat-integer-properties/video/828

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 36 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 30 first replies
5 GMATGuruNY 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

91 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

56 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

35 posts
See More Top Beat The GMAT Experts