GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Apr 2019, 11:07

### 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 unique factors does 96 have?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54495
How many unique factors does 96 have?  [#permalink]

### Show Tags

08 Jul 2017, 05:38
00:00

Difficulty:

5% (low)

Question Stats:

84% (00:49) correct 16% (01:22) wrong based on 137 sessions

### HideShow timer Statistics

How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

_________________
Manager
Joined: 23 May 2017
Posts: 239
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: How many unique factors does 96 have?  [#permalink]

### Show Tags

08 Jul 2017, 05:41
prime factors of 96 = 2^5 * 3 = number of factors = 6 * 2 = 12

Ans= C
_________________
If you like the post, please award me Kudos!! It motivates me
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: How many unique factors does 96 have?  [#permalink]

### Show Tags

08 Jul 2017, 05:53
1
1
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

$$n = a^p*b^q$$ -------------- ($$a$$ and $$b$$ are prime factors of $$n$$ and $$p$$ and $$q$$ are their powers)

Number of factors of $$n$$ will be expressed by formula $$(p+1)(q+1)$$

Prime factors of $$96 = 2^5 * 3^1$$

Number of unique factors $$= (5+1)(1+1) = 6*2 = 12$$

Senior SC Moderator
Joined: 22 May 2016
Posts: 2651
How many unique factors does 96 have?  [#permalink]

### Show Tags

08 Jul 2017, 07:32
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

For me, learning the method was a lot easier than remembering the formula (kudos to sashiim20 ), so

1. Find prime factors of 96 =>
2*2*2*2*2*3, or $$2^53^1$$

2. Take the power of each prime factor and add 1

5+1 = 6 and
1+1= 2

3. Multiply results: 6*2 = 12, which includes all of the distinct factors of 96 including 96 and 1.

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
CEO
Joined: 12 Sep 2015
Posts: 3589
Re: How many unique factors does 96 have?  [#permalink]

### Show Tags

08 Jul 2017, 07:42
Top Contributor
Bunuel wrote:
How many unique factors does 96 have?

A. 8
B. 10
C. 12
D. 14
E. 15

The posters above have used a useful rule (which I am providing a video for below). However, if you weren't aware of that rule, you can always just list the factors.

When doing so, find pairs, starting from the lowest and biggest factors. We get:

Factors of 96: {1, 96}
Factors of 96: {1, 2, 48, 96}
Factors of 96: {1, 2, 3, 32, 48, 96}
.
.
.
and so on..
.
Factors of 96: {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}
12 factors

RELATED VIDEOS

_________________
Test confidently with gmatprepnow.com
Re: How many unique factors does 96 have?   [#permalink] 08 Jul 2017, 07:42
Display posts from previous: Sort by