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

It is currently 22 Oct 2014, 04:13

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 integers can be factors of 78? (do it without

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2769
Location: New York City
Followers: 8

Kudos [?]: 253 [0], given: 4

how many integers can be factors of 78? (do it without [#permalink] New post 08 Nov 2007, 01:19
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:
Senior Manager
Senior Manager
avatar
Joined: 19 Feb 2007
Posts: 328
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: factors [#permalink] New post 08 Nov 2007, 04:53
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


4
I'm not listing the factors
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 889
Followers: 6

Kudos [?]: 169 [0], given: 33

 [#permalink] New post 08 Nov 2007, 05:23
1,2,3 and 13!!

Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?
Director
Director
User avatar
Joined: 03 May 2007
Posts: 899
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 52 [0], given: 7

Re: factors [#permalink] New post 08 Nov 2007, 09:24
sidbidus wrote:
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


4
I'm not listing the factors


Are you guys doping prime factorization? it is asking only factors not different prime factors. so i guess it should be 8.

1, 2, 3, 6, 13, 26, 39, 78.
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2769
Location: New York City
Followers: 8

Kudos [?]: 253 [0], given: 4

 [#permalink] New post 08 Nov 2007, 09:38
LM wrote:
1,2,3 and 13!!

Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?


this is a variation of one of the Challenges.


we get the prime factors of 78:

2 *39
2* 3* 13

Now here's where it gets nice. :P
we look at the exponents of each of the factors and add one.
2, 2, 2

we multiply all the modified exponents together= 2*2*2=8 factors in all
Intern
Intern
avatar
Joined: 31 Oct 2007
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 08 Nov 2007, 10:56
factors of 78

78 = 2 * 39

so (1+1)* (1+1) = 2*2 = 4
total four factors.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 6

Kudos [?]: 108 [0], given: 0

 [#permalink] New post 09 Nov 2007, 17:31
LM wrote:
1,2,3 and 13!!

Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?


http://www.gmatclub.com/forum/t55022
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 51 [0], given: 0

Re: factors [#permalink] New post 09 Nov 2007, 18:35
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


something i have noticed, unless it is a perfect square (ex. 4 or 25) integer must have EVEN # of factors

i get 8:
1,2,3,6,13,26,39,78

using the method that bkk145's shown me:

prime factorization
2*3*13
(1+1)(1+1)(1+1) = 8

either way its 8
Director
Director
avatar
Joined: 09 Aug 2006
Posts: 767
Followers: 1

Kudos [?]: 52 [0], given: 0

Re: factors [#permalink] New post 10 Nov 2007, 00:13
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


If the prime factorization of an integer is a^n * b^m * c^p, then the number of factors that integer has = (n+1)(m+1)(p+1).

In this case that gives us 8 factors.
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1156
Followers: 6

Kudos [?]: 118 [0], given: 0

Re: factors [#permalink] New post 10 Nov 2007, 00:18
GK_Gmat wrote:
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


If the prime factorization of an integer is a^n * b^m * c^p, then the number of factors that integer has = (n+1)(m+1)(p+1).

In this case that gives us 8 factors.


Perfect !

:)
Intern
Intern
avatar
Joined: 14 Nov 2007
Posts: 11
Followers: 0

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

Re: factors [#permalink] New post 17 Nov 2007, 19:20
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


Sorry, but I'm a little confused. I came across a similar problem and had trouble with your method. The question is how many positive intergers are factors of 441?
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1156
Followers: 6

Kudos [?]: 118 [0], given: 0

Re: factors [#permalink] New post 17 Nov 2007, 21:43
Ant wrote:
bmwhype2 wrote:
how many integers can be factors of 78? (do it without tediously listing the factors) :lol:


Sorry, but I'm a little confused. I came across a similar problem and had trouble with your method. The question is how many positive intergers are factors of 441?


factor 441

441 | 7

63 | 3

21 | 7

3

3^2*7^2 = (2+1)*(2+1) = 9

:)
Senior Manager
Senior Manager
User avatar
Joined: 09 Oct 2007
Posts: 468
Followers: 1

Kudos [?]: 19 [0], given: 1

 [#permalink] New post 17 Nov 2007, 23:21
can someone explain this method with apples and oranges please?
I get lost after finding the prime factors. :oops:
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3571
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 367

Kudos [?]: 1850 [1] , given: 358

GMAT ToolKit User Premium Member
 [#permalink] New post 17 Nov 2007, 23:56
1
This post received
KUDOS
Expert's post
asdert wrote:
can someone explain this method with apples and oranges please?
I get lost after finding the prime factors. :oops:


it is very good that
a^n * b^m * c^p => Nf = (n+1)(m+1)(p+1). (a,b,c -prime numbers)

why is it correct?

one has such cases: {a^0,a^1,.......a^n}*{b^0,b^1,......b^m}*{c^0,c^1,......c^p}
therefore, for a - n+1 (from 1=a^0 to a^n)
b - m+1
c - p+1

Nf=(n+1)(m+1)(p+1)
Senior Manager
Senior Manager
User avatar
Joined: 09 Oct 2007
Posts: 468
Followers: 1

Kudos [?]: 19 [0], given: 1

 [#permalink] New post 18 Nov 2007, 09:46
So, is this correct then?

Factors of 60:

60/2
30/2
15/3
5


2² * 3 * 5, therefore (2+1)(1+1(1+1) = 12

Outcome number includes 1 and itself, correct? awesome! thanks for the tip.
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1156
Followers: 6

Kudos [?]: 118 [0], given: 0

 [#permalink] New post 18 Nov 2007, 10:01
asdert wrote:
So, is this correct then?

Factors of 60:

60/2
30/2
15/3
5


2² * 3 * 5, therefore (2+1)(1+1(1+1) = 12

Outcome number includes 1 and itself, correct? awesome! thanks for the tip.


Yes {60,30,20,15,12,10,6,5,4,3,2,1} = 12

:)
Senior Manager
Senior Manager
User avatar
Joined: 09 Oct 2007
Posts: 468
Followers: 1

Kudos [?]: 19 [0], given: 1

 [#permalink] New post 18 Nov 2007, 11:45
Does this holds tru for any number or are there any exceptions? I've tested it on a bunch and all seem to be ok.

How come this stuff is not on any study guide?

I thought Mgmat was going to cover all this important tricks. I guess that's why the forum rocks.

Is there a thread somewhere with tips like this? (not necessarily factors related)

Thanks!
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1156
Followers: 6

Kudos [?]: 118 [0], given: 0

 [#permalink] New post 18 Nov 2007, 12:44
asdert wrote:
Does this holds tru for any number or are there any exceptions? I've tested it on a bunch and all seem to be ok.

How come this stuff is not on any study guide?

I thought Mgmat was going to cover all this important tricks. I guess that's why the forum rocks.

Is there a thread somewhere with tips like this? (not necessarily factors related)

Thanks!


I think that walker gave a very good proof for this.

:)
  [#permalink] 18 Nov 2007, 12:44
    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic How many factors does the integer X have? eladshush 13 04 Oct 2010, 05:16
1 How many times can I take the GMAT without penalty? snkrhed 3 06 May 2010, 01:17
5 Experts publish their posts in the topic How many words, with or without meaning can be made from the zaarathelab 19 28 Dec 2009, 02:25
1 How many different positive integers are factors of 441? lumone 4 02 Mar 2008, 13:01
How many numbers can be a FACTOR of 90 Riuscita 7 04 Apr 2006, 21:21
Display posts from previous: Sort by

how many integers can be factors of 78? (do it without

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.