GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 26 May 2020, 20:09

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.

Close

Request Expert Reply

Confirm Cancel

How many positive integers are factors of 216, inclusive of 1 and the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
D
Joined: 29 Oct 2019
Posts: 307
How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 20 Mar 2020, 18:45
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:12) correct 17% (01:22) wrong based on 24 sessions

HideShow timer Statistics

How many positive integers are factors of 216, inclusive of 1 and the number itself?

(A) 9

(B) 12

(C) 16

(D) 18

(E) 24
Manager
Manager
avatar
B
Joined: 18 Dec 2017
Posts: 205
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 20 Mar 2020, 19:05
216=2^3×3^3
No of factors = 4×4 =16

Posted from my mobile device
Intern
Intern
User avatar
B
Joined: 14 Jan 2020
Posts: 29
GMAT 1: 760 Q51 V41
How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 21 Mar 2020, 00:46
2
total no of factors of integer \(n = a^x * b^y\) where a, b are prime factors is given by \((x+1)*(y+1)\)
\(216= 2^3 * 3^3\) thus no of factors are \((3+1)*(3+1)=16\)
ANSWER : C
_________________
PREP NOW!!
START YOUR MBA JOURNEY WITH
GLOBAL COLLEGE INFO : admin@globalcollegeinfo.com
CONTACT US FOR HELP WITH PROFILE BUILDING AND TEST PREP
BOTH ARE INTEGRAL PARTS OF YOUR APPLICATION>
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3367
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 21 Mar 2020, 08:31

Solution



To find
We need to determine
    • The number of positive factors of 216, including 1 and 216

Approach and Working out
Expressing 216 in terms of its prime factors, we get:
    • \(216 = 8 * 27 = 2^3 * 3^3\)
    • Hence, total number of factors of 216 = (3 + 1) x (3 + 1) = 4 x 4 = 16

Thus, option C is the correct answer.

Correct Answer: Option C
_________________
Manager
Manager
avatar
B
Joined: 18 Dec 2017
Posts: 205
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 21 Mar 2020, 18:45
What if we have to find odd factors?

Posted from my mobile device
Director
Director
User avatar
D
Joined: 16 Jan 2019
Posts: 598
Location: India
Concentration: General Management
WE: Sales (Other)
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

Show Tags

New post 21 Mar 2020, 19:11
gurmukh wrote:
What if we have to find odd factors?

Posted from my mobile device


If we need just the number of odd factors, the prime factor 2 can take only one power which is 0 and the prime factor 3 can take 4 powers which are 0,1,2 and 3

So total number of odd factors = 1*4 = 4

Total number of even factors = 16-4 = 12

Hope this helps
GMAT Club Bot
Re: How many positive integers are factors of 216, inclusive of 1 and the   [#permalink] 21 Mar 2020, 19:11

How many positive integers are factors of 216, inclusive of 1 and the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne