NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 10:20 It is currently 23 Apr 2024, 10:20
Decision Tracker
My Rewards
New posts
New comers' posts

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

How many factors does the integer 9999 have?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
HarveyS
Manager
Manager
Joined: 14 Jan 2013
Posts: 114
Own Kudos [?]: 1527 [26]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Send PM
How many factors does the integer 9999 have? [#permalink] New post   22 Mar 2014, 02:26
6
Kudos
20
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

66% (01:31) correct 34% (01:42) wrong based on 507 sessions
Hide Show timer Statistics
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [20]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: How many factors does the integer 9999 have? [#permalink] New post   22 Mar 2014, 04:43
10
Kudos
10
Bookmarks
Expert Reply
Mountain14 wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15


Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

BACK TO THE ORIGINAL QUESTION:

\(9999 = 3^2*11*101\) --> the number of factors is (2+1)(1+1)(1+1)=12.

Answer: D.
General Discussion
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [2]
Given Kudos: 275
Re: How many factors does the integer 9999 have? [#permalink] New post   10 Jan 2017, 23:39
2
Kudos
9999 can also be written as (10000-1)

(10000-1)= ((10^4)- 1)= ((10^2)^2 - 1)

Applying (a^2-b^2)= (a+b) (a-b)

(10^2+1) (10^2-1)= 101*99= 101*3^2*11

Number of factors= (1+1)(2+1)(1+1)= 2*3*2= 12
User avatar
hangovrlyf
Intern
Intern
Joined: 22 Dec 2013
Posts: 12
Own Kudos [?]: 16 [0]
Given Kudos: 98
Send PM
GMAT ToolKit User
Re: How many factors does the integer 9999 have? [#permalink] New post   26 Apr 2014, 11:16
+1 for D :lol: , concept mentioned in GMATClub QUANT BOOK....do read to brushup basic and advance quant topics :idea:
avatar
sanket1991
Manager
Manager
Joined: 14 Sep 2014
Posts: 74
Own Kudos [?]: 95 [0]
Given Kudos: 51
WE:Engineering (Consulting)
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   26 Nov 2014, 03:53
9999 = 3^2 * 11 * 101
and hence 2*2*3 = 12 distinct factors
User avatar
pacifist85
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 340
Own Kudos [?]: 386 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
How many factors does the integer 9999 have? [#permalink] New post   24 Feb 2015, 13:58
We start with the prime factorization, as shown in the illustration.

Then, to find the number of factors, we add one to each of the powers and multply these additions.

So,

(2+1)*(1+1)*(1+1)
3*2*2
12

So, there are 12 factors in total.
Attachments

factorization.png
factorization.png [ 1.65 KiB | Viewed 15942 times ]

avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1367 [0]
Given Kudos: 23
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   28 Feb 2015, 08:04
Expert Reply
Mountain14 wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15


Factorise 9999 = 3 * 3 * 11 * 101
= 3^2 * 11^1 * 101^1
Number of factors = (2+1)(1+1)(1+1)
= 3*2*2
=12
Hence option D.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
User avatar
B
ak1802
Manager
Manager
Joined: 26 May 2013
Posts: 80
Own Kudos [?]: 65 [0]
Given Kudos: 32
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   01 Mar 2015, 09:18
So 9 has 3 factors.

9 appears 4 times in the number.

4(3) = 12.

I checked this method with a few different numbers, all consiting of repeated integers less than 10 and it worked.

88

8 has 4 factors therefore 88 has 4(2)= 8.

Can anyone confirm that this works?

Posted from my mobile device
User avatar
G
colorblind
Manager
Manager
Joined: 30 Dec 2015
Posts: 58
Own Kudos [?]: 118 [0]
Given Kudos: 173
GPA: 3.92
WE:Engineering (Aerospace and Defense)
Send PM
How many factors does the integer 9999 have? [#permalink] New post   25 Oct 2016, 17:50
ak1802 wrote:
So 9 has 3 factors.

9 appears 4 times in the number.

4(3) = 12.

I checked this method with a few different numbers, all consiting of repeated integers less than 10 and it worked.

88

8 has 4 factors therefore 88 has 4(2)= 8.

Can anyone confirm that this works?

Posted from my mobile device


Interesting.....but didnt work for 777.
avatar
B
GMATAcademy
Manager
Manager
Joined: 25 Jun 2016
Posts: 58
Own Kudos [?]: 546 [0]
Given Kudos: 4
GMAT 1: 780 Q51 V46
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   07 Jan 2017, 08:17
I, for one, find it much easier to retain a formula if I understand it. Here's a video that goes over the logic behind the formula some of the responses are using:

User avatar
L
AkshdeepS
VP
VP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1479
Own Kudos [?]: 1600 [0]
Given Kudos: 1002
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Send PM
Reviews Badge
Re: How many factors does the integer 9999 have? [#permalink] New post   31 May 2018, 23:30
HarveyS wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15


9999 = 3 * 3 * 11 * 101

Add 1 to powers of all prime factors and multiply:

(2+1) (1+1) (1+1)

3*2*2

12

(D)
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6269 [0]
Given Kudos: 1646
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   03 Jun 2018, 18:29
Expert Reply
HarveyS wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15



Breaking 9999 into primes we have:

9999 = 9 x 1111 = 9 x 101 x 11 = 3^2 x 101^1 x 11^1

So the total number of factors is (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12.

Answer: D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32624
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: How many factors does the integer 9999 have? [#permalink] New post   29 Mar 2023, 09:13
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
gmatclubot
Re: How many factors does the integer 9999 have? [#permalink]
29 Mar 2023, 09:13
Moderators:
Bunuel
Math Expert
92875 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions