What is the least number that should be multiplied to 100! : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 15:56

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the least number that should be multiplied to 100!

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
VP
Joined: 30 Sep 2004
Posts: 1488
Location: Germany
Followers: 6

Kudos [?]: 327 [0], given: 0

What is the least number that should be multiplied to 100! [#permalink]

### Show Tags

06 May 2005, 09:05
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?

(1) 144
(2) 72
(3) 108
(4) 216
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Manager
Joined: 22 Apr 2005
Posts: 129
Location: Los Angeles
Followers: 1

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

Re: PS - least number [#permalink]

### Show Tags

06 May 2005, 09:29
christoph wrote:
What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?

(1) 144
(2) 72
(3) 108
(4) 216

Let's count 3s in prime factoring of 100!

Multiples of 3 - 33
Among them multiples of 3^2=9 - 11
Among them multiples of 3^3=27 - 3
Among them multiples of 3^4 = 81 - 1

Total 4*1 + 2*3 + 8 * 2 + 22 * 1 = 48

We need at least another 3^2 = 9

72 = 3^2 * 2^3 - the least number that we need.

Answear (2).
VP
Joined: 26 Apr 2004
Posts: 1218
Location: Taiwan
Followers: 2

Kudos [?]: 608 [0], given: 0

### Show Tags

06 May 2005, 15:22
one multiple of 3: 3,6,9,.......99 (33)

two multiples of 3: 9,18,27,36,.....99 (11)

three multiples of 3: 27,54, 81 (3)

four multiples of 3: 81 (1)

total: 48

Hence, we need 2 additional multiples of 3.

72 is the least
Senior Manager
Joined: 21 Mar 2004
Posts: 444
Location: Cary,NC
Followers: 3

Kudos [?]: 68 [0], given: 0

### Show Tags

06 May 2005, 16:52
The numbers are from 1 to 100

The biggest number is 99. Lets remove the numbers which are factors of 3 and list them after factoring.

99 = 33 * 3
96 = 32 * 3
.
.
3 = 1 * 3

So,
3 3 3 3 3 3 3 3 3..........3 3 3 3 = total 33 times 3 is a factor
1 2 34 5 6.....32...33= total 11 time 3 appears once more (33/3)

....9........18.........27 = total 3 times 3 appears twice
.................... 27 = total 1 time 3 appears thrice

total 48 times it appears.........only 2 more required...ie smallest number having 9 as a factor is 72.
_________________

ash
________________________
I'm crossing the bridge.........

06 May 2005, 16:52
Display posts from previous: Sort by

# What is the least number that should be multiplied to 100!

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.