NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 08:48 It is currently 25 Apr 2024, 08:48
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 positive integers will divide evenly into 520?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618957 [7]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
How many positive integers will divide evenly into 520? [#permalink] New post   21 Apr 2016, 00:31
2
Kudos
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

67% (01:10) correct 33% (01:37) wrong based on 193 sessions
Hide Show timer Statistics
How many positive integers will divide evenly into 520?

A. 8
B. 12
C. 16
D. 18
E. 20
ShowHide Answer
Official Answer
C
avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1367 [2]
Given Kudos: 23
Send PM
Re: How many positive integers will divide evenly into 520? [#permalink] New post   21 Apr 2016, 02:44
2
Bookmarks
Expert Reply
Bunuel wrote:
How many positive integers will divide evenly into 520?

A. 8
B. 12
C. 16
D. 18
E. 20


520 = 10*13*4 = 8*5*13 = 2^3*5*13

We need to positive integers will divide evenly into 520 or simply the factors of 520

If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)

Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 16

Option C
User avatar
G
TarPhi
Manager
Manager
Joined: 24 Sep 2019
Posts: 128
Own Kudos [?]: 91 [0]
Given Kudos: 171
Location: India
GMAT 1: 710 Q49 V36
Send PM
Reviews Badge
Re: How many positive integers will divide evenly into 520? [#permalink] New post   27 Oct 2020, 18:49
What does divide evenly really mean?

It is not, no. of even divisors, right?

Bunuel
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31922 [1]
Given Kudos: 290
Send PM
Reviews Badge
Re: How many positive integers will divide evenly into 520? [#permalink] New post   27 Oct 2020, 20:21
1
Kudos
Expert Reply
TarPhi wrote:
What does divide evenly really mean?

It is not, no. of even divisors, right?

Bunuel



Here evenly is not related to even-odd. Evenly means equally, so factors that completely divide 520 without leaving decimals.
Example.
9 is evenly divisible by 1,3 and 9.
But 7 is not evenly divisible by 3 as it leads to a remainder 1.
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31922 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: How many positive integers will divide evenly into 520? [#permalink] New post   27 Oct 2020, 20:36
Expert Reply
Bunuel wrote:
How many positive integers will divide evenly into 520?

A. 8
B. 12
C. 16
D. 18
E. 20



For finding factors, either use the formula or calculate for each factor, a method that can be time consuming.

Formula
Get the number into its prime factor.
520 =2*5*52=2*5*2*26=2*2*2*5*13\(2^3*5*13\)
Number of factors = (3+1)(1+1)(1+1)=4*2*2=16

Calculate
520=1*520=2*260=4*130=5*104=8*65=10*52=13*40=20*26
So 1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
16

C
User avatar
G
TarPhi
Manager
Manager
Joined: 24 Sep 2019
Posts: 128
Own Kudos [?]: 91 [0]
Given Kudos: 171
Location: India
GMAT 1: 710 Q49 V36
Send PM
Reviews Badge
Re: How many positive integers will divide evenly into 520? [#permalink] New post   27 Oct 2020, 21:29
Thank chetan2u

Just to confirm no. of factors is 16.

If they had asked
no of odd factors, it would've been 4
no of even factors, it would've been 12

Yeah?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31922 [2]
Given Kudos: 290
Send PM
Reviews Badge
Re: How many positive integers will divide evenly into 520? [#permalink] New post   27 Oct 2020, 21:39
1
Kudos
1
Bookmarks
Expert Reply
TarPhi wrote:
Thank chetan2u

Just to confirm no. of factors is 16.

If they had asked
no of odd factors, it would've been 4
no of even factors, it would've been 12

Yeah?



Yes,

Odd factors will consist of 5*13, so (1+1)(1+1)=4
Even factors = 16-4=12
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18760
Own Kudos [?]: 22051 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: How many positive integers will divide evenly into 520? [#permalink] New post   31 Oct 2020, 13:47
Expert Reply
Bunuel wrote:
How many positive integers will divide evenly into 520?

A. 8
B. 12
C. 16
D. 18
E. 20

Solution:

Since we need to determine the number of factors of 520, we need to prime factorize 520:

520 = 52 x 10 = 4 x 13 x 2 x 5 = 2^3 x 5^1 x 13^1

The number of positive factors of any integer is obtained by adding 1 to each exponent of the integer’s prime factorization and then multiplying those “adjusted” exponent numbers. Thus, we see that 520 has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 factors.

Answer: C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32675
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: How many positive integers will divide evenly into 520? [#permalink] New post   03 Oct 2023, 09:06
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 positive integers will divide evenly into 520? [#permalink]
03 Oct 2023, 09:06
Moderators:
Bunuel
Math Expert
92914 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