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

It is currently 23 Oct 2014, 02:28

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

3^X is the greatest positive divisor of 10!*20!*30!. Find X

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 53 [0], given: 0

3^X is the greatest positive divisor of 10!*20!*30!. Find X [#permalink] New post 05 May 2003, 05:16
3^X is the greatest positive divisor of 10!*20!*30!. Find X.
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 53 [0], given: 0

 [#permalink] New post 05 May 2003, 05:24
YeSS! :banana
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 53 [0], given: 0

 [#permalink] New post 20 May 2003, 02:27
I think there is a mistake here. I have decided to use Excel to check the problem and got that 3^90 is the largest divisor.

WHY?
Manager
Manager
avatar
Joined: 12 Mar 2003
Posts: 59
Followers: 1

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

 [#permalink] New post 20 May 2003, 04:14
What's the trick on this one
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 53 [0], given: 0

 [#permalink] New post 20 May 2003, 04:16
Logically 26 is OK, but Excel does not agree. I don't know why.
Manager
Manager
avatar
Joined: 12 Mar 2003
Posts: 59
Followers: 1

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

 [#permalink] New post 20 May 2003, 04:20
In Excel I get 62.5. How did you get 26 ?
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 53 [0], given: 0

 [#permalink] New post 20 May 2003, 04:40
10!=1*2*3*4*5*6*7*8*9*10

multiples of 3 are: 3, 6=2*3, 9=3*3. so there are 4 threes, or 3^4.

20! includes the above 3^4, plus threes in 12, 15, 18, other 3^4. Total 3^8

30! includes the above 3^8, plus threes in 21, 24, 27(3^3), 30. Total 3^14.

Overall, 3^(4+8+14)=3^26 -- the largest divisor.

Seems OK, but Excel does not agree
Senior Manager
Senior Manager
avatar
Joined: 03 Nov 2005
Posts: 399
Location: Chicago, IL
Followers: 3

Kudos [?]: 25 [0], given: 17

 [#permalink] New post 16 Dec 2005, 21:06
x=4+8+14=26

1) 10/3=3 2)20/3=6 3)30/3=10
3/3=1 6/3=2 10/3=3
1/3=0 2/3=0 3/3=1
1/3=0
_________________

Hard work is the main determinant of success

  [#permalink] 16 Dec 2005, 21:06
    Similar topics Author Replies Last post
Similar
Topics:
What is the greatest common divisor of positive integers m marcodonzelli 3 12 Mar 2008, 12:05
What is the greatest common divisor of positive intigers m M8 5 14 May 2006, 04:06
What is the greatest common divisor of positive integers m gmat_crack 5 08 Apr 2006, 20:36
meaning of greatest positive divisor cloaked_vessel 2 06 Jan 2005, 13:25
What is the greatest common divisor of positive integers m twixt 4 22 Nov 2004, 06:50
Display posts from previous: Sort by

3^X is the greatest positive divisor of 10!*20!*30!. Find X

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.