GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 May 2020, 22:08

### 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 p is an integer and 3^p is a factor of 300!, what is the maximum

Author Message
TAGS:

### Hide Tags

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3253
Location: India
GPA: 3.12
If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 11:33
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:25) correct 47% (02:00) wrong based on 103 sessions

### HideShow timer Statistics

If p is an integer and 3^p is a factor of 300!, what is the maximum possible value of p?

A.100
B.101
C.133
D.147
E.148

Source: Experts Global

_________________
You've got what it takes, but it will take everything you've got
Current Student
Joined: 12 Aug 2015
Posts: 2522
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 11:49
1
1
Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]

Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.
_________________
VP
Joined: 09 Mar 2016
Posts: 1235
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 11:59
stonecold wrote:
Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]

Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.

Hi stonecold i think you smashed correctly

can you please advice (if you know any) some article about how to solve such kind of questions "3^p is a factor of 300!"

i had no idea how to approach it,

thanks!
Intern
Joined: 20 Nov 2017
Posts: 16
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 16:32
Can this method be used as 2^n aswell?

Sent from my SM-N910C using GMAT Club Forum mobile app
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3253
Location: India
GPA: 3.12
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 20:42
1
Hey ra5867 & dave13

https://gmatclub.com/forum/everything-a ... 85592.html

Under this, you will find the detailed explanation under
Finding the powers of a prime number p, in the n!

Hope this helps!
_________________
You've got what it takes, but it will take everything you've got
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4990
Location: India
GPA: 3.5
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 22:29
pushpitkc wrote:
If p is an integer and 3^p is a factor of 300!, what is the maximum possible value of p?

A.100
B.101
C.133
D.147
E.148

Source: Experts Global

$$\frac{300}{3} = 100$$
$$\frac{100}{3} = 33$$
$$\frac{33}{3} = 11$$
$$\frac{11}{3} = 3$$
$$\frac{3}{3} = 1$$

So, the maximum possible value of p will be 100 + 33 + 11 + 3 + 1 = 148 , answer must be (E)

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Math Expert
Joined: 02 Sep 2009
Posts: 64068
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 22:31
ra5867 wrote:
Can this method be used as 2^n aswell?

Sent from my SM-N910C using GMAT Club Forum mobile app

Everything about Factorials on the GMAT
Power of a Number in a Factorial Problems
Trailing Zeros Problems

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10436
Location: Pune, India
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

21 Jan 2018, 23:02
dave13 wrote:
stonecold wrote:
Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]

Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.

Hi stonecold i think you smashed correctly

can you please advice (if you know any) some article about how to solve such kind of questions "3^p is a factor of 300!"

i had no idea how to approach it,

thanks!

Check this post for a detailed discussion:
https://www.veritasprep.com/blog/2011/0 ... actorials/
_________________
Karishma
Veritas Prep GMAT Instructor

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3253
Location: India
GPA: 3.12
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

28 Jan 2018, 10:20

Official Explanation by Experts Global

_________________
You've got what it takes, but it will take everything you've got
Non-Human User
Joined: 09 Sep 2013
Posts: 14969
Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

### Show Tags

06 Aug 2019, 04:04
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 p is an integer and 3^p is a factor of 300!, what is the maximum   [#permalink] 06 Aug 2019, 04:04