Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 May 2016, 16:37
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many distinct positive factors does 30,030 have?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 16 Apr 2009
Posts: 16
Followers: 0

Kudos [?]: 9 [0], given: 5

How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 18 Dec 2012, 04:07
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:25) correct 40% (01:27) wrong based on 153 sessions

HideShow timer Statictics

How many distinct positive factors does 30,030 have?

A. 16
B. 32
C. 64
D. 128
E. 256
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Dec 2012, 04:26, edited 1 time in total.
Moved to PS forum and added OA.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68390 [1] , given: 9797

Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 18 Dec 2012, 04:30
1
This post received
KUDOS
Expert's post
Drik wrote:
How many distinct positive factors does 30,030 have?

A. 16
B. 32
C. 64
D. 128
E. 256


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 OT THE ORIGINAL QUESTION:

Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #2 and 7. Thank you.
_________________

New to the Math Forum?
Please read this: 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9248
Followers: 454

Kudos [?]: 115 [0], given: 0

Premium Member
Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 08 Feb 2015, 19:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 18 Aug 2014
Posts: 97
Location: United States
GMAT 1: 710 Q42 V46
GPA: 3.13
Followers: 0

Kudos [?]: 6 [0], given: 63

GMAT ToolKit User Reviews Badge CAT Tests
How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 13:38
Bunuel wrote:

Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.


How does one do this aspect quickly?
_________________

Please help me find my lost Kudo's bird

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 12 Sep 2015
Posts: 334
Location: Canada
Followers: 21

Kudos [?]: 224 [1] , given: 4

Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 15:12
1
This post received
KUDOS
1
This post was
BOOKMARKED
redfield wrote:
Bunuel wrote:

Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.


How does one do this aspect quickly?


Here's a free video lesson on finding the prime factorization of a number: http://www.gmatprepnow.com/module/gmat- ... /video/825
Here's a free video lesson that explains why Bunuel's formula works: http://www.gmatprepnow.com/module/gmat- ... /video/828

Cheers,
Brent
_________________

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with:
- over 500 videos (35 hours of instruction)
- over 800 practice questions
- 2 full-length practice tests and other bonus offers
- http://www.gmatprepnow.com/

Manager
Manager
avatar
Joined: 18 Aug 2014
Posts: 97
Location: United States
GMAT 1: 710 Q42 V46
GPA: 3.13
Followers: 0

Kudos [?]: 6 [0], given: 63

GMAT ToolKit User Reviews Badge CAT Tests
Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 18:47
GMATPrepNow wrote:

Here's a free video lesson on finding the prime factorization of a number: http://www.gmatprepnow.com/module/gmat- ... /video/825
Here's a free video lesson that explains why Bunuel's formula works: http://www.gmatprepnow.com/module/gmat- ... /video/828

Cheers,
Brent


I appreciate the videos which were informative however they don't really answer my specific question; I'm not asking about how to find the # of divisors, I'm wondering how (and this wasn't explained in either video) you quickly figure our the prime factors of a massive number like 30,030?

In the video the question is 14,000 and he just skips to "and here are the prime factors" and I don't get how you figure that out in a timely manner.
_________________

Please help me find my lost Kudo's bird

Senior Manager
Senior Manager
User avatar
Joined: 12 Sep 2015
Posts: 334
Location: Canada
Followers: 21

Kudos [?]: 224 [0], given: 4

How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 19:17
redfield wrote:
GMATPrepNow wrote:

Here's a free video lesson on finding the prime factorization of a number: http://www.gmatprepnow.com/module/gmat- ... /video/825
Here's a free video lesson that explains why Bunuel's formula works: http://www.gmatprepnow.com/module/gmat- ... /video/828

Cheers,
Brent


I appreciate the videos which were informative however they don't really answer my specific question; I'm not asking about how to find the # of divisors, I'm wondering how (and this wasn't explained in either video) you quickly figure our the prime factors of a massive number like 30,030?

In the video the question is 14,000 and he just skips to "and here are the prime factors" and I don't get how you figure that out in a timely manner.


At 1:30 in the video http://www.gmatprepnow.com/module/gmat- ... /video/825, we explain the process using a tree diagram. The process works for ANY number.

Cheers
Brent
_________________

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with:
- over 500 videos (35 hours of instruction)
- over 800 practice questions
- 2 full-length practice tests and other bonus offers
- http://www.gmatprepnow.com/

Manager
Manager
avatar
Joined: 18 Aug 2014
Posts: 97
Location: United States
GMAT 1: 710 Q42 V46
GPA: 3.13
Followers: 0

Kudos [?]: 6 [0], given: 63

GMAT ToolKit User Reviews Badge CAT Tests
Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 19:26
GMATPrepNow wrote:
At 1:30 in the video http://www.gmatprepnow.com/module/gmat- ... /video/825, we explain the process using a tree diagram. The process works for ANY number.

Cheers
Brent


So you see 14,000 and have to do a factor tree starting with a number you can eyeball like 140 and 100 then continue breaking those numbers down?

I'm sorry if I'm missing something here (feel like I'm definitely overcomplicating or simply not getting a simple idea); but when I see a number like 30,030 and one of the steps is "30,030 = 2*3*5*7*11*13" it seems like I'm missing an entire part of the explanation because it seems the speed people are getting these primes would be something more streamlined than a factor tree. It's possible it's just a matter of practice makes it faster I just wasn't sure if I was missing an entire step.

Thank you for the explanations.
_________________

Please help me find my lost Kudo's bird

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 12 Sep 2015
Posts: 334
Location: Canada
Followers: 21

Kudos [?]: 224 [2] , given: 4

Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 19 Nov 2015, 21:00
2
This post received
KUDOS
redfield wrote:
GMATPrepNow wrote:
At 1:30 in the video http://www.gmatprepnow.com/module/gmat- ... /video/825, we explain the process using a tree diagram. The process works for ANY number.

Cheers
Brent


So you see 14,000 and have to do a factor tree starting with a number you can eyeball like 140 and 100 then continue breaking those numbers down?

I'm sorry if I'm missing something here (feel like I'm definitely overcomplicating or simply not getting a simple idea); but when I see a number like 30,030 and one of the steps is "30,030 = 2*3*5*7*11*13" it seems like I'm missing an entire part of the explanation because it seems the speed people are getting these primes would be something more streamlined than a factor tree. It's possible it's just a matter of practice makes it faster I just wasn't sure if I was missing an entire step.

Thank you for the explanations.


Start with 30,030
I can see this is divisible by 10.
So, 30,030 = (3003)(10)
Or 30,030 = (3003)(2)(5)
What about 3003?
Well, the sum of the digits is 6, and 6 is divisible by 3, which means 3003 is divisible by 3 (this in an important divisibility rule that's discussed in this free video: http://www.gmatprepnow.com/module/gmat- ... /video/822 )
So, 30,030 = (3)(1001)(2)(5)
This is where it gets a bit tricky since it's hard to see any PRIME divisors of 1001. We know that 2, 3 and 5 don't work. What about 7?
When we check we get: 1001 = (7)(143)

So, 30,030 = (3)(7)(143)(2)(5)
Finally, 143 = ...
So, 30,030 = (3)(7)(11)(13)(2)(5)

Cheers,
Brent
_________________

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with:
- over 500 videos (35 hours of instruction)
- over 800 practice questions
- 2 full-length practice tests and other bonus offers
- http://www.gmatprepnow.com/

Manager
Manager
avatar
Joined: 18 Aug 2014
Posts: 97
Location: United States
GMAT 1: 710 Q42 V46
GPA: 3.13
Followers: 0

Kudos [?]: 6 [0], given: 63

GMAT ToolKit User Reviews Badge CAT Tests
How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 20 Nov 2015, 08:40
GMATPrepNow wrote:

Start with 30,030
I can see this is divisible by 10.
So, 30,030 = (3003)(10)
Or 30,030 = (3003)(2)(5)
What about 3003?
Well, the sum of the digits is 6, and 6 is divisible by 3, which means 3003 is divisible by 3 (this in an important divisibility rule that's discussed in this free video: http://www.gmatprepnow.com/module/gmat- ... /video/822 )
So, 30,030 = (3)(1001)(2)(5)
This is where it gets a bit tricky since it's hard to see any PRIME divisors of 1001. We know that 2, 3 and 5 don't work. What about 7?
When we check we get: 1001 = (7)(143)

So, 30,030 = (3)(7)(143)(2)(5)
Finally, 143 = ...
So, 30,030 = (3)(7)(11)(13)(2)(5)

Cheers,
Brent


Thank you very much for breaking it down like this, it was a simple matter of the task appearing more daunting to me than it actually was so this step-by-step was perfect thank you Brent.
_________________

Please help me find my lost Kudo's bird

Director
Director
User avatar
Joined: 12 Aug 2015
Posts: 671
Followers: 11

Kudos [?]: 49 [0], given: 149

GMAT ToolKit User CAT Tests
Re: How many distinct positive factors does 30,030 have? [#permalink]

Show Tags

New post 16 Mar 2016, 01:15
Here 1001 is divisible by 11
thats the only basic problem to be solved actually
and also the number of +ve divisors = product of powers of primes after increase them by 1
Re: How many distinct positive factors does 30,030 have?   [#permalink] 16 Mar 2016, 01:15
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic How many positive distinct prime factors does 5^20 + 5^17 have? pbarrocas 4 04 Dec 2014, 01:32
11 Experts publish their posts in the topic How many factors does the integer 9999 have? Mountain14 7 22 Mar 2014, 02:26
32 Experts publish their posts in the topic How many factors does 36^2 have? enigma123 9 22 Jan 2012, 16:48
9 Experts publish their posts in the topic How many factors does 36^2 have? praveengmat 9 15 Aug 2010, 03:47
9 Experts publish their posts in the topic How many factors does 36^2 have? GMATT73 42 13 Nov 2006, 07:58
Display posts from previous: Sort by

How many distinct positive factors does 30,030 have?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.