Last visit was: 22 Apr 2026, 11:57 It is currently 22 Apr 2026, 11:57
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,751
Own Kudos:
810,648
 [10]
Given Kudos: 105,821
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: 109,751
Kudos: 810,648
 [10]
A certain number N is divisible by the product of the first fourteen 26 Apr 2016, 00:58
2
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

70% (02:20) correct 30% (02:06) wrong based on 277 sessions

History

Date
Time
Result
Not Attempted Yet
A certain number N is divisible by the product of the first fourteen positive integers. Which of the following must be a factor of N?

A. 1,690
B. 1,210
C. 726
D. 625
E. 616
ShowHide Answer
Official Answer
E
User avatar
arirux92
User avatar
Joined: 03 May 2015
Last visit: 30 Nov 2016
Posts: 121
Own Kudos:
246
 [2]
Given Kudos: 23
Location: South Africa
Concentration: International Business, Organizational Behavior
Schools: Rotman '21 Melbourne '18 (M) Thunderbird Fall '21 IE '22
GPA: 3.49
WE:Web Development (Insurance)
Schools: Rotman '21 Melbourne '18 (M) Thunderbird Fall '21 IE '22
Posts: 121
Kudos: 246
 [2]
A certain number N is divisible by the product of the first fourteen 26 Apr 2016, 03:41
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A certain number N is divisible by the product of the first fourteen positive integers. Which of the following must be a factor of N?

A. 1,690
B. 1,210
C. 726
D. 625
E. 616
Show more

So... n is a multiple of 14! So prime numbers till 14 have occurred only once.

a) 1690 .... two 13s; out
b) 1210 .. two 11s; out
D) 625 ... 25^2 ... four 5s... but we have got only 2 ( 5 and 10)
c) 726 = 6 * 121 = two 11s (only 1 there in 14!)

Without even calculating, I can easily mark E.

But still, for peace of mind : 616 = 8 * 77 = 8*7*11 ( we have all of them)
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,904
Own Kudos:
5,449
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,904
Kudos: 5,449
A certain number N is divisible by the product of the first fourteen 26 Apr 2016, 08:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A certain number N is divisible by the product of the first fourteen positive integers. Which of the following must be a factor of N?

A. 1,690
B. 1,210
C. 726
D. 625
E. 616
Show more

The number is 14!

We are asked to the factor of the number....

Check the options -

A. 1,690 = 2^1 x 5^1 x 13^2 ; 14! will have only one 13 , so 1690 can't be a factor of 14!

B. 1,210 = 2^1 x 5^1 x 11^2; 14! will have only one 11 , so 1210 can't be a factor of 14!

C. 726 = 2^1 x 3^1 x 11^2; 14! will have only one 11 , so 726 can't be a factor of 14!

D. 625 = 5^4

No of 5's in 14! is 2 , so 625 can't be a factor of 14!

14/5 = 2
2/5 = 0

E. 616 = 2^3 x 7^1 x 11^1

14! will have 11 two's

14/2 = 7
7/2 = 3
3/2 = 1

Hence answer will be (E)
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,231
Own Kudos:
3,643
 [2]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,231
Kudos: 3,643
 [2]
A certain number N is divisible by the product of the first fourteen 02 May 2016, 20:38
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
I have solved many Questions of this kind.
A general helping tip => Start with E .
Also i read a post on the MGMAT forum that said => in elimination questions the order - B,D,E,A,C is the way to go.
though i still Dont know why that is...! (maybe its a probability thing )
User avatar
rhine29388
User avatar
Joined: 24 Nov 2015
Last visit: 21 Oct 2019
Posts: 386
Own Kudos:
146
Given Kudos: 231
Location: United States (LA)
Products:
My Reviews
Posts: 386
Kudos: 146
A certain number N is divisible by the product of the first fourteen 07 May 2016, 13:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Basically the problem is finding the factor of 14!
1690 = 2*5*13*13 (two 13's eliminate)
1210 = 2*5*11*11 (two 11's eliminate)
726 = 2*3*11*11 (two 11's eliminate)
625 = 5*5*5*5 (only two 5's in 14!)
616 = 2*2*2*7*11(all factors are present in 14!)
correct answer - E
User avatar
adkikani
User avatar
IIM School Moderator
Joined: 04 Sep 2016
Last visit: 24 Dec 2023
Posts: 1,223
Own Kudos:
1,359
 [1]
Given Kudos: 1,207
Location: India
WE:Engineering (Other)
Posts: 1,223
Kudos: 1,359
 [1]
A certain number N is divisible by the product of the first fourteen 25 Aug 2018, 18:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel VeritasKarishma chetan2u gmatbusters niks18 GMATPrepNow

I understood above approaches, but almost all above methods requires prime factorization of
three digits numbers and consumed more time. Any alternate approach to solve this efficiently?
User avatar
niks18
User avatar
Retired Moderator
Joined: 25 Feb 2013
Last visit: 30 Jun 2021
Posts: 862
Own Kudos:
1,805
 [3]
Given Kudos: 54
Location: India
GPA: 3.82
Products:
My Reviews
Posts: 862
Kudos: 1,805
 [3]
A certain number N is divisible by the product of the first fourteen 25 Aug 2018, 18:55
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
adkikani
Bunuel VeritasKarishma chetan2u gmatbusters niks18 GMATPrepNow

I understood above approaches, but almost all above methods requires prime factorization of
three digits numbers and consumed more time. Any alternate approach to solve this efficiently?
Show more

Hi adkikani

N is divisible by 14!. 14! contains only one 11 & 13 and N has to be even because 14! is even

Now look at the option

1690 = 169*10, 169 is square of 13 hence this will contain two 13's. therefore not a factor of N
1210 = 121*10, 121 is square of 11 hence this will contain two 11's. therefore not a factor of N
625 = 625 is square of 25 hence this will contain two 25's. therefore not a factor of N

726, is divisible by 11 (remember the divisibility rule for 11), the resulting number will again be divisible by 11. hence this also contains two or more 11s. Reject this

So your final answer has to be Option E.

If you remember the square and divisibility rule then this question can be solved within 30s by just skimming at the options
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
44,993
 [1]
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: 44,993
 [1]
A certain number N is divisible by the product of the first fourteen 25 Aug 2018, 19:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
adkikani
Bunuel VeritasKarishma chetan2u gmatbusters niks18 GMATPrepNow

I understood above approaches, but almost all above methods requires prime factorization of
three digits numbers and consumed more time. Any alternate approach to solve this efficiently?
Show more

Hi

Since question involves product and then asks us for the choice that has to be a factor, it will require prime factorization and I doubt you can do this without Getting into factorization.
If you know certain squares as also suggested above, it can avoid complete factorization, but yes you have to factor the choices.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,966
Own Kudos:
1,117
Posts: 38,966
Kudos: 1,117
A certain number N is divisible by the product of the first fourteen 25 Mar 2026, 19:45
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
109751 posts
Krunaal
Tuck School Moderator
853 posts