Last visit was: 21 Jul 2024, 00:29 It is currently 21 Jul 2024, 00:29
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94433
Own Kudos [?]: 642623 [8]
Given Kudos: 86715
Send PM
Most Helpful Reply
Senior Manager
Senior Manager
Joined: 13 Oct 2016
Posts: 299
Own Kudos [?]: 781 [5]
Given Kudos: 40
GPA: 3.98
Send PM
General Discussion
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6049
Own Kudos [?]: 4767 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22685 [2]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: What is the greatest value of d such that 6^d is a factor of 18! ? [#permalink]
2
Kudos
Expert Reply
Bunuel wrote:
What is the greatest value of d such that 6^d is a factor of 18! ?

A. 3
B. 4
C. 5
D. 6
E. 8


We need to determine the maximum value of d such that 18!/(6^d) is an integer. We must remember that an integer is divisible by 6 if it’s divisible by both 3 and 2. Thus, we must determine the number of factors of 2 and 3 in 18!. However, since we know there are fewer factors of 3 than factors of 2 in 18!, we can find the number of factors of 3 and thus be able to determine the maximum value of d.

To determine the number of factors of 3 within 18!, we can use the following shortcut in which we divide 18 by 3, and then divide the quotient of 18/3 by 3 and continue this process until we no longer get a nonzero quotient:

18/3 = 6

6/3 = 2

Since 2/3 does not produce a nonzero quotient, we can stop.

The final step is to add up our quotients; that sum represents the number of factors of 3 within 18!. Thus, there are 6 + 2 = 8 factors of 3 within 18!, and the maximum value of d is 8.

Answer: E
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34040
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: What is the greatest value of d such that 6^d is a factor of 18! ? [#permalink]
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.
GMAT Club Bot
Re: What is the greatest value of d such that 6^d is a factor of 18! ? [#permalink]
Moderator:
Math Expert
94433 posts