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

 It is currently 25 Apr 2015, 23:41

### 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

# Find the largest power of 12 that can divide 200! a. 97 b.

Author Message
TAGS:
Senior Manager
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

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

Find the largest power of 12 that can divide 200! a. 97 b. [#permalink]  07 Jan 2004, 12:34
Find the largest power of 12 that can divide 200!

a. 97
b. 98
c. 17
e. None of these

***I got answer choice (e), but official answer disagrees. Just making sure here. The answer should be 88. RIght?
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

I can't think of an easy way to do this question.

In one through 200

100 numbers are multiples of two
50 numbers are multiples of four
25 numbers are multiples of eight
12 numbers are multiples of 16
6 numbers are multiples of 32
3 numbers are multiples of 64
1 number is a multiple of 128

2^197

66 numbers are multiples of three
22 numbers are multiples of nine
7 numbers are multiples of 27
3 numbers are multiples of 51
1 number is a multiple of 153

3^98

since you need two twos and a three to make 12, and there are more than twice as many twos as threes, the threes are the limiting parameter.

98?

I could be terribly wrong...
Senior Manager
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

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

An simpler method of attacking this question:

Since 12 is an even #, take the prime factorization: 2^2 *3
Now, 200/2 leaves 'Q'uotient 100, 100/2 leaves Q 50, 50/2 leaves Q 25, 25/2 leaves Q 12, 12/2 leaves Q 6, 6/2 leaves Q 3, 3/2 leaves Q 1
Now, add up all the quotients: 100+50+25+12+6+3+1 = 197
2^2 is two twoos, so divide 197 by 2 = Qoutient 98

Now do the same with 200/3. Add up all quotients. If the total is larger than 98. 98 is the answer. If the total is smaller than 98, the smaller # is the answer. I realized my mistake. I made an error with computing the quotients above when I did it before. The official answer is correct. You will find that when you get the quotients from 200/3 the total will yield 97.
97 is smaller than 98, so it is the answer.
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Director
Joined: 14 Oct 2003
Posts: 588
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

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

sunniboy007 wrote:
An simpler method of attacking this question:

Since 12 is an even #, take the prime factorization: 2^2 *3
Now, 200/2 leaves 'Q'uotient 100, 100/2 leaves Q 50, 50/2 leaves Q 25, 25/2 leaves Q 12, 12/2 leaves Q 6, 6/2 leaves Q 3, 3/2 leaves Q 1
Now, add up all the quotients: 100+50+25+12+6+3+1 = 197
2^2 is two twoos, so divide 197 by 2 = Qoutient 98

Now do the same with 200/3. Add up all quotients. If the total is larger than 98. 98 is the answer. If the total is smaller than 98, the smaller # is the answer. I realized my mistake. I made an error with computing the quotients above when I did it before. The official answer is correct. You will find that when you get the quotients from 200/3 the total will yield 97.
97 is smaller than 98, so it is the answer.

Is that really a simple approach? I'm not trying to be sarcastic but I still don't understand your approach.

This is how i view the problem:
200! assume - it's a big number!! obviously - you need something close to a super computer to calculate this number.
but we do know that it's even, it's greater than 12^98 (the largest answer choice) and it ends in lots of zeros (thus, it's even!).

so any number that ends with 0,2,5,4 and 8 will divide evenly into this number.

just like powers of 2 we can do the same for powers of 12

2^1=2 2^5=32 12^1=12
2^2=4 2^6=64 12^2=144
2^3=8 2^7=128 etc.
2^4=16 2^8=256

Thus use the powers of 2 as a proxy for the powers of 12 since the pattern repeats itself after the 4th power

thus the 97th power ends in 8 - thus 12^97 can divide evenly into 200! the 98th power ends in 6 so that would end in .6666667

Thus 12^97 is your answer - one of those problems that you can solve under 1.5 mins. if you see the patterns!
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

Nice work, Titleist.
Director
Joined: 14 Oct 2003
Posts: 588
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

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

stoolfi wrote:
Nice work, Titleist.

Thanks Stoolfi. You haven't changed your avatar yet!
Similar topics Replies Last post
Similar
Topics:
6 Three is the largest number that can be divided evenly into 2 24 Sep 2012, 19:06
2 What is the largest power of 3 contained in 200! 5 24 Oct 2010, 10:29
Find the maximum power of 6 which will divide 65! A) 11 B) 15 22 Jun 2007, 00:52
What is the largest power of 55 that can divide 274! 12 15 Sep 2006, 03:28
What is the largest prime number that can divide evenly into 9 16 Oct 2005, 00:02
Display posts from previous: Sort by