Last visit was: 31 May 2026, 05:20 It is currently 31 May 2026, 05:20
Home
Messages
MBA Fair
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
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 31 May 2026
Posts: 1,847
Own Kudos:
2,730
 [3]
Given Kudos: 232
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,847
Kudos: 2,730
 [3]
How many positive integers have more than 3 positive divisor 11 Apr 2026, 02:00
Kudos
Add Kudos
3
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:

95% (hard)

Question Stats:

40% (02:54) correct 60% (02:54) wrong based on 48 sessions

History

Date
Time
Result
Not Attempted Yet
How many positive integers have more than 3 positive divisors and are factors of 1,800?

(A) 24
(B) 26
(C) 27
(D) 29
(E) 30
ShowHide Answer
Official Answer
D
User avatar
percyboi66
User avatar
Joined: 02 Feb 2026
Last visit: 28 May 2026
Posts: 12
Own Kudos:
5
Given Kudos: 2
Location: India
Schools: Duke Fuqua LBS NYU Stern HEC
GPA: 6.3
Schools: Duke Fuqua LBS NYU Stern HEC
Posts: 12
Kudos: 5
How many positive integers have more than 3 positive divisor 11 Apr 2026, 03:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I got the correct answer (D) but had to take a very roundabout way by basically writing down all the factors of 1800, is there a quicker way?
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 31 May 2026
Posts: 1,847
Own Kudos:
2,730
Given Kudos: 232
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,847
Kudos: 2,730
How many positive integers have more than 3 positive divisor 12 Apr 2026, 08:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If \(p\) is a prime number, how many divisors does \(p^2\) have?
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 31 May 2026
Posts: 1,847
Own Kudos:
2,730
Given Kudos: 232
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,847
Kudos: 2,730
How many positive integers have more than 3 positive divisor 13 Apr 2026, 01:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From the total number of factors, subtract the number that have at most three positive divisors.
User avatar
Adit_
User avatar
Joined: 04 Jun 2024
Last visit: 30 May 2026
Posts: 822
Own Kudos:
275
Given Kudos: 141
Posts: 822
Kudos: 275
How many positive integers have more than 3 positive divisor 13 Apr 2026, 01:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Use the formula for total number of factors of a number by prime factorizing.

1800 = 2^3*3^2*5^2.
Total factors = 4*3*3 = 36.

Now you need to remove those factors whose number of factors of those factors are 3 or less than 3.
When does that happen?
When you have a^2 form or just a form. Every other face you will have more than 3 factors for that factor.
Also dont forget about 1.

Now from prime factorization of 1800 we can remove the single factors ie- 2,3,5 which is 3.
We should also remove a^2 form which are 2^2,3^2,5^2 which is another 3.
Including 1 it is 3+3+1 = 7 factors removed.

Final answer = 36-7 = 29.
percyboi66
I got the correct answer (D) but had to take a very roundabout way by basically writing down all the factors of 1800, is there a quicker way?
Show more
User avatar
pappal
User avatar
Joined: 24 Nov 2022
Last visit: 29 May 2026
Posts: 336
Own Kudos:
111
Given Kudos: 115
Posts: 336
Kudos: 111
How many positive integers have more than 3 positive divisor 14 May 2026, 13:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total factors of (1800=2^3*3^2*5^2)=36
out of these ones which don't have more than 3 factors are,1,2,3,4,5,9 & 25
hence required ones=36-7=29
D
User avatar
Ravisoni
User avatar
Joined: 23 Jul 2024
Last visit: 15 May 2026
Posts: 4
Given Kudos: 1
Posts: 4
Kudos: 0
How many positive integers have more than 3 positive divisor 15 May 2026, 01:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sol:

As, 1800=2^3 x 3^2 x5^2
Total factors= 4x3x3 = 36
No. of Prime factor(i.e 2,3,5) = 3 (having 3 positive divisors)
No. of Prime factor(i.e 4,9,25) = 3 (having 3 positive divisors)
Ans = Total factors - prime factors-square of prime factor - 1(1 having only 1 divisor)
= 36 - 3- 3 - 1 = 29 (D)
Moderator:
Bunuel
Math Expert
110986 posts