GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Sep 2018, 23:08

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

2,600 has how many positive divisors?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 277
2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 28 Oct 2010, 17:10
1
10
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (00:44) correct 32% (00:55) wrong based on 400 sessions

HideShow timer Statistics

2,600 has how many positive divisors?

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

_________________

I'm the Dumbest of All !!

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49275
Re: divsors  [#permalink]

Show Tags

New post 29 Oct 2010, 03:11
3
5
ulm wrote:
vgan4 wrote:
Number of factors = (3+1)(2+1)(1+1)=24


can' t understand how we came to this. What does this multiplication mean?


Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Back to the original question:
If p and q are prime numbers, how many divisors does the product \(p^3*q^6\) have?

According to above the number of distinct factors of \(2,600=2^3*5^2*13\) would be \((3+1)(2+1)(1+1)=24\).

For more on this check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 26 Sep 2010
Posts: 11
Re: divsors  [#permalink]

Show Tags

New post 28 Oct 2010, 17:21
1
By factorization, you can write 2600 as 2600=2^3*5^2*13^1. Number of factors = (3+1)(2+1)(1+1)=24
Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 149
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
GMAT ToolKit User Reviews Badge
Re: divsors  [#permalink]

Show Tags

New post 29 Oct 2010, 02:47
vgan4 wrote:
Number of factors = (3+1)(2+1)(1+1)=24


can' t understand how we came to this. What does this multiplication mean?
Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 149
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
GMAT ToolKit User Reviews Badge
Re: divsors  [#permalink]

Show Tags

New post 29 Oct 2010, 03:27
Yes, thanks,
i forgot
"The number of factors of n will be expressed by the formula \((p+1)(q+1)(r+1)\)"
Senior Manager
Senior Manager
User avatar
B
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 451
Location: India
Premium Member
Re: 2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 20 Mar 2017, 01:27
shrive555 wrote:
2,600 has how many positive divisors?

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


2600 = 13 x 2^3 x 5^2

no of possible divisor = (1+1)(2+1)(3+1) = 4.3.2 = 24

Option D
_________________

GMAT Mentors
Image

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 721
Premium Member
Re: 2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 03 Apr 2017, 00:16
2600= 26*100= 2*13*2^2*5^2
=2^3*5^2*13

Total factors= (3+1)(2+1)(1+1)= 4*3*2=24
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: 2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 05 Jan 2018, 11:24
shrive555 wrote:
2,600 has how many positive divisors?

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


To determine the number of positive divisors, we break 2,600 into primes, add 1 to the exponent of each unique prime, and then multiply those values together.

We see that 2,600 = 26 x 100 = 2 x 13 x 4 x 25 = 2^3 x 5^2 x 13^1.

Now we add 1 to each exponent and multiply those results:

(3 + 1)(2 + 1)(1 +1) = 24

Thus, 2,600 has 24 positive divisors.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2864
Location: Canada
2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 05 Jan 2018, 11:56
Top Contributor
1
shrive555 wrote:
2,600 has how many positive divisors?

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


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-------------------------

2600 = (2)(2)(2)(5)(5)(13)
= (2^3)(5^2)(13^1)
So, the number of positive divisors of 2600 = (3+1)(2+1)(1+1) =(4)(3)(2) = 24

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

2,600 has how many positive divisors? &nbs [#permalink] 05 Jan 2018, 11:56
Display posts from previous: Sort by

2,600 has how many positive divisors?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.