Last visit was: 24 Apr 2026, 13:50 It is currently 24 Apr 2026, 13:50
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
foragge1234
User avatar
Joined: 06 Dec 2022
Last visit: 19 Dec 2022
Posts: 1
Own Kudos:
17
 [17]
Given Kudos: 6
Posts: 1
Kudos: 17
 [17]
What is the greatest integer value of n such that 9^n is a factor 17 Dec 2022, 00:04
1
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

58% (01:55) correct 42% (02:18) wrong based on 165 sessions

History

Date
Time
Result
Not Attempted Yet
What is the greatest integer value of n such that \(9^n\) is a factor of 43! + 44!

A) 22

B) 18

C) 16

D) 10

E) 9
ShowHide Answer
Official Answer
D
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 24 Apr 2026
Posts: 11,229
Own Kudos:
45,009
 [3]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,009
 [3]
What is the greatest integer value of n such that 9^n is a factor 17 Dec 2022, 03:40
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
foragge1234
What is the greatest integer value of n such that \(9^n\) is a factor of 43! + 44!

A) 22

B) 18

C) 16

D) 10

E) 9
Show more

\(43!+44!=43!(1+44)=43!*45\)

Now 43! Will have \(\frac{43}{3}+\frac{43}{3^2}+\frac{43}{3^3}=14+4+1=19\)

Thus, total number of \(9^n\) or \(3^{2n}\) = \(\frac{19+2}{2}= \frac{21}{2}\) or 10­
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 24 Apr 2026
Posts: 5,986
Own Kudos:
5,859
 [3]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,986
Kudos: 5,859
 [3]
What is the greatest integer value of n such that 9^n is a factor 17 Dec 2022, 08:40
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: What is the greatest integer value of n such that \(9^n\) is a factor of 43! + 44!

43! + 44! = 43! (1+44) = 43! * 45 = 9*5*43!

Highest power of 3 in 43! = 14 + 4 + 1 = 19
Highest power of 9 in 43! = 9
Highest power of 9 in (43! + 44! = 9*5*43!) = 9+1 = 10

IMO D
User avatar
HarshaBujji
User avatar
Joined: 29 Jun 2020
Last visit: 24 Apr 2026
Posts: 723
Own Kudos:
907
 [1]
Given Kudos: 247
Location: India
Products:
My Reviews
Posts: 723
Kudos: 907
 [1]
What is the greatest integer value of n such that 9^n is a factor 18 Dec 2022, 06:57
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
foragge1234
What is the greatest integer value of n such that \(9^n\) is a factor of 43! + 44!

A) 22

B) 18

C) 16

D) 10

E) 9
Show more


To find the max power of any num we need to see the prime factors of the number.

Here its 3, Max power is 10.

IMO D
User avatar
stne
User avatar
Joined: 27 May 2012
Last visit: 23 Apr 2026
Posts: 1,809
Own Kudos:
2,090
 [2]
Given Kudos: 679
Posts: 1,809
Kudos: 2,090
 [2]
What is the greatest integer value of n such that 9^n is a factor 19 Dec 2022, 12:02
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
foragge1234
What is the greatest integer value of n such that \(9^n\) is a factor of 43! + 44!

A) 22

B) 18

C) 16

D) 10

E) 9
Show more

\(9^n = 3^{2n}\)

\(43! + 44! = 43! (1+44)\)

=\(43!45\)

There are two parts \(43! \) and \(45 \) we have to find the highest power of \(3\) in both the parts

In \(43!\) highest power of \(3 \)

\(\frac{43}{3} = 14\)

\(\frac{14}{3} = 4\)

\(\frac{4}{3} =1\)

\(14+4+1 = 19\) ...(I)

in \(45 \) hightest power of \(3\):

\(45 = 3*3*5 \) -> highest power of three is \( 2\) ...(II)

Thus highest power of three = \(19+ 2 = 21\)... (I)+(II)

But this has to be equated to \(2n\)

Hence \(2n=21 \)

\(n=10.5 \)

So highest power of \(3\) in \(3^{2n} = 10\)

Ans D

Hope it helped.
User avatar
skmaan
User avatar
Joined: 16 Mar 2023
Last visit: 26 Mar 2026
Posts: 26
Own Kudos:
5
Given Kudos: 20
Location: India
Concentration: General Management, Finance
Schools: Darden '26
GPA: 7.84
WE:Project Management (Consulting)
Schools: Darden '26
Posts: 26
Kudos: 5
What is the greatest integer value of n such that 9^n is a factor 05 Jun 2024, 01:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why can it not be solved like the following?

43! (45) / 9^n

43! will have 43/9 (4) ; 43/18 (2) ; 43/27 (1) ; 43/36 (1)
(Multiples of 9)

Adding: 4 + 0 + 2 + 1 + 1 + (1 from 45) = 9 ; what other 9 am i missing ; why is this approach incorrect ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,065
 [1]
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,818
Kudos: 811,065
 [1]
What is the greatest integer value of n such that 9^n is a factor 06 Jun 2024, 01:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skmaan
Why can it not be solved like the following?

43! (45) / 9^n

43! will have 43/9 (4) ; 43/18 (2) ; 43/27 (1) ; 43/36 (1)
(Multiples of 9)

Adding: 4 + 0 + 2 + 1 + 1 + (1 from 45) = 9 ; what other 9 am i missing ; why is this approach incorrect ?
Show more

For one, this method is used to find the power of a prime in a factorial; you cannot apply it to a non-prime. Also, for primes, we use the powers of the prime in the denominator, not the multiples.
User avatar
shadow04
User avatar
Joined: 08 Aug 2023
Last visit: 12 Apr 2025
Posts: 6
Own Kudos:
2
Given Kudos: 20
Location: United States
Posts: 6
Kudos: 2
What is the greatest integer value of n such that 9^n is a factor 19 Aug 2024, 21:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is there a reason why we cannot solve it the following way? (FYI: Incorrect answer)

What is the greatest integer value of n such that 9^n is a factor translates to:
(43! + 44!)/(9^n)

Split it since the denominator is the same:

((43!)/(9^n)) + ((44!)/(9^n))

Calculate the number of 3's in each part.

43! = 19; Since it's 2n, n<=9
44! = 19; Since it's 2n, n<=9

Add 9 + 9 = 18. Yes, it's wrong, but I don't know why ...
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,974
Own Kudos:
1,117
Posts: 38,974
Kudos: 1,117
What is the greatest integer value of n such that 9^n is a factor 15 Nov 2025, 14:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts