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

 It is currently 01 Jun 2020, 08:07

### 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

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

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Oct 2019
Posts: 314
How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

### Show Tags

20 Mar 2020, 18:45
1
00:00

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
Joined: 18 Dec 2017
Posts: 211
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

### Show Tags

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

Posted from my mobile device
Intern
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

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 $$(3+1)*(3+1)=16$$
_________________
PREP NOW!!
BOTH ARE INTEGRAL PARTS OF YOUR APPLICATION>
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3394
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

### Show Tags

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.

_________________
Manager
Joined: 18 Dec 2017
Posts: 211
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

### Show Tags

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

Posted from my mobile device
Director
Joined: 16 Jan 2019
Posts: 608
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

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