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

It is currently 19 Jun 2019, 00:07

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: 256
2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 28 Oct 2010, 17:10
2
10
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:04) correct 28% (01:25) wrong based on 440 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: 55681
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.
_________________
General Discussion
Intern
Intern
avatar
Joined: 26 Sep 2010
Posts: 10
Re: divsors  [#permalink]

Show Tags

New post 28 Oct 2010, 17:21
2
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: 142
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: 142
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 \((p+1)(q+1)(r+1)\)"
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
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: 657
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: 2823
Re: 2,600 has how many positive divisors?  [#permalink]

Show Tags

New post 05 Jan 2018, 11:24
1
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
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3783
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
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
2,600 has how many positive divisors?   [#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  


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