GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 04:22

### 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

# If 15!/3^m is an integer, what is the greatest possible value of m?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58428
If 15!/3^m is an integer, what is the greatest possible value of m?  [#permalink]

### Show Tags

13 Mar 2019, 00:45
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:45) correct 28% (01:29) wrong based on 81 sessions

### HideShow timer Statistics

If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

_________________
VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If 15!/3^m is an integer, what is the greatest possible value of m?  [#permalink]

### Show Tags

13 Mar 2019, 00:50
Bunuel wrote:
If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

15/3 = 5

15/9 = 1

Total number of 3's in 15! = 6.

C is the correct answer.

For more , check out club's material .
https://gmatclub.com/forum/math-number- ... 88376.html
Manager
Joined: 15 Jan 2018
Posts: 60
If 15!/3^m is an integer, what is the greatest possible value of m?  [#permalink]

### Show Tags

10 Apr 2019, 08:11
1
2
What is the question really asking here?

It's simply asking: For the quotient to be an integer, we need the same number of factors of 3 in the numerator as we need in the denominator. So our task here is to find how many factors of 3 are in the numerator, which means the denominator could have just as many to maintain that the quotient is an integer.

So $$\frac{15!}{3^m}$$ is really $$\frac{15*14*13*12*11*10*9.....}{3*3*3*3.....}$$

The question asks for the max number of 3's in the denominator. We already established, for the quotient to be an integer, we need to figure out how many 3's are in the numerator!

So simply count the factors of 3. That's 3, 6, 9, 12, 15... So that's 5 factors!! Nope, 9 has 2 factors of 3, so 6 factors.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8125
Location: United States (CA)
Re: If 15!/3^m is an integer, what is the greatest possible value of m?  [#permalink]

### Show Tags

13 Apr 2019, 18:35
Bunuel wrote:
If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

Breaking down the primes of 3 within 15! we have:

3

6 = 3 x 2

9 = 3^2

12 = 2^2 x 3

15 = 3 x 5

We see that there are 6 factors of 3 in 15!, and thus the maximum value of m is 6.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13388
Re: If 15!/3^m is an integer, what is the greatest possible  [#permalink]

### Show Tags

02 May 2019, 01:27
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.
_________________
Re: If 15!/3^m is an integer, what is the greatest possible   [#permalink] 02 May 2019, 01:27
Display posts from previous: Sort by

# If 15!/3^m is an integer, what is the greatest possible value of m?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne