Last visit was: 21 Apr 2026, 12:05 It is currently 21 Apr 2026, 12:05
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
SandhyAvinash
User avatar
Joined: 05 Oct 2016
Last visit: 19 Sep 2019
Posts: 68
Own Kudos:
136
 [45]
Given Kudos: 135
Location: United States (OH)
Schools: CBS '20 Fisher '20 Kelley '20
GPA: 3.58
Schools: CBS '20 Fisher '20 Kelley '20
Posts: 68
Kudos: 136
 [45]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 09:51
4
Kudos
Add Kudos
41
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:

75% (hard)

Question Stats:

56% (02:32) correct 44% (02:14) wrong based on 463 sessions

History

Date
Time
Result
Not Attempted Yet
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,729
Own Kudos:
810,446
 [13]
Given Kudos: 105,798
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: 109,729
Kudos: 810,446
 [13]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 10:15
7
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6
Show more

4k + 2 = 2(2k + 1) = 2*odd. So, we are looking for even factors which are not multiples of 4.

180 = 2^2*3^2*5. Consider the part without 2^2. Now, 3^2*5 has (2 + 1)(1 + 1) = 6 factors: 1, 3, 5, 9, 15, 45. Any of them paired with 2 will be even factor of 180 which is not a multiple of 4, so 2, 6, 10, 18, 30 and 90.

Answer: E.
General Discussion
User avatar
SandhyAvinash
User avatar
Joined: 05 Oct 2016
Last visit: 19 Sep 2019
Posts: 68
Own Kudos:
136
 [2]
Given Kudos: 135
Location: United States (OH)
Schools: CBS '20 Fisher '20 Kelley '20
GPA: 3.58
Schools: CBS '20 Fisher '20 Kelley '20
Posts: 68
Kudos: 136
 [2]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 16:36
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6

4k + 2 = 2(2k + 1) = 2*odd. So, we are looking for even factors which are not multiples of 4.

180 = 2^2*3^2*5. Consider the part without 2^2. Now, 3^2*5 has (2 + 1)(1 + 1) = 6 factors: 1, 3, 5, 9, 15, 45. Any of them paired with 2 will be even factor of 180 which is not a multiple of 4, so 2, 6, 10, 18, 30 and 90.

Answer: E.
Show more

Bunuel how did you find 6 factors as 1,3,5,9,15,45. please help me in this.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,729
Own Kudos:
810,446
 [3]
Given Kudos: 105,798
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: 109,729
Kudos: 810,446
 [3]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 20:30
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
SandhyAvinash
Bunuel
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6

4k + 2 = 2(2k + 1) = 2*odd. So, we are looking for even factors which are not multiples of 4.

180 = 2^2*3^2*5. Consider the part without 2^2. Now, 3^2*5 has (2 + 1)(1 + 1) = 6 factors: 1, 3, 5, 9, 15, 45. Any of them paired with 2 will be even factor of 180 which is not a multiple of 4, so 2, 6, 10, 18, 30 and 90.

Answer: E.

Bunuel how did you find 6 factors as 1,3,5,9,15,45. please help me in this.
Show more

I just manually listed the factors of 90 = 3^2*5. You don't have to find the factors for this question though, it's done here just to illustrate. The fact that 90 has 6 factors (does not matter what they really are) is enough to get that 180 will have twice as many even factors which are not multiples of 4.
avatar
Spongebob02
avatar
Joined: 09 Aug 2017
Last visit: 07 May 2018
Posts: 20
Own Kudos:
1
 [1]
Posts: 20
Kudos: 1
 [1]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 21:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6

4k + 2 = 2(2k + 1) = 2*odd. So, we are looking for even factors which are not multiples of 4.

180 = 2^2*3^2*5. Consider the part without 2^2. Now, 3^2*5 has (2 + 1)(1 + 1) = 6 factors: 1, 3, 5, 9, 15, 45. Any of them paired with 2 will be even factor of 180 which is not a multiple of 4, so 2, 6, 10, 18, 30 and 90.

Answer: E.
Show more
How did you got (2+1)(1+1) ?? Pls explain

Sent from my Redmi 3S using GMAT Club Forum mobile app
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,729
Own Kudos:
810,446
 [4]
Given Kudos: 105,798
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: 109,729
Kudos: 810,446
 [4]
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 Dec 2017, 21:16
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Spongebob02
Bunuel
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6

4k + 2 = 2(2k + 1) = 2*odd. So, we are looking for even factors which are not multiples of 4.

180 = 2^2*3^2*5. Consider the part without 2^2. Now, 3^2*5 has (2 + 1)(1 + 1) = 6 factors: 1, 3, 5, 9, 15, 45. Any of them paired with 2 will be even factor of 180 which is not a multiple of 4, so 2, 6, 10, 18, 30 and 90.

Answer: E.
How did you got (2+1)(1+1) ?? Pls explain

Sent from my Redmi 3S using GMAT Club Forum mobile app
Show more

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.

2. Properties of Integers




5. Divisibility/Multiples/Factors



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
avatar
Angelponce
avatar
Joined: 04 Jul 2018
Last visit: 27 Dec 2020
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
Find the number of factors of 180 that are in the form (4*k + 2), wher 04 Aug 2018, 21:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
There are 6 possibilities, where f(x)=4x+2 is a factor of 180.

f(0)=2
F(1)=6
f(2)=10
f(4)=18
f(7)=30
f(22)=80
User avatar
adstudy
User avatar
Joined: 11 Mar 2018
Last visit: 15 Dec 2023
Posts: 248
Own Kudos:
437
Given Kudos: 270
Location: India
GMAT 1: 710 Q49 V37 (Online)
GMAT 1: 710 Q49 V37 (Online)
Posts: 248
Kudos: 437
Find the number of factors of 180 that are in the form (4*k + 2), wher 04 Aug 2018, 22:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SandhyAvinash
Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?

A)1
B)2
C)3
D)4
E)6
Show more

I did this question with simple substitution like below -

we know K >=0 and is an integer.

therefore for
K = 0 ; (4*k + 2) = 2 - A factor of 180
K = 1 ; (4*k + 2) = 6 - A factor of 180
K = 2 ; (4*k + 2) = 10 - A factor of 180
K = 4 ; (4*k + 2) = 18 - A factor of 180

No we know answer can be D or E.

If I am able to find one more my answer will be E.

Hence I factorized 180 = 2x3x3x2x5

Next number after 18 I can form is 30 that will be a factor of 180 and I get that with k = 7.

Hence E.

FYI - I did this question under two minutes. So IMO not a lengthy method.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,953
Own Kudos:
1,117
Posts: 38,953
Kudos: 1,117
Find the number of factors of 180 that are in the form (4*k + 2), wher 12 May 2025, 23:29
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
109729 posts
Krunaal
Tuck School Moderator
853 posts