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

 It is currently 18 Sep 2018, 10:40

### 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

# What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1182
Location: India
WE: General Management (Aerospace and Defense)
What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15  [#permalink]

### Show Tags

Updated on: 24 Sep 2017, 21:40
Top Contributor
1
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:45) correct 27% (00:46) wrong based on 112 sessions

### HideShow timer Statistics

What is the Greatest Common Factor (GCF) of $$18x^8y^{(20)}$$ and $$24x^{(12)}y^{(15)}$$?

A. $$3x^4y^5$$

B. $$6x^4y^5$$

C. $$3x^8y^{(15)}$$

D. $$6x^8y^{(15)}$$

E. $$72x^{(12)}y^{(20)}$$

_________________

Originally posted by Gnpth on 24 Sep 2017, 21:30.
Last edited by Bunuel on 24 Sep 2017, 21:40, edited 1 time in total.
Renamed the topic and edited the question.
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3128
Location: India
GPA: 3.12
Re: What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15  [#permalink]

### Show Tags

25 Sep 2017, 04:12
The GCF of numbers 18 and 24 is 6.
Therefore the answer must be either Option B or D

The reason why our answer option is Option D because
$$x^8y^{(15)}$$ can be multiplied with $$y^5$$ and $$x^4$$ to give $$x^8y^{(20)}$$ and $$x^{(12)}y^{(15)}$$ & Option D is bigger than Option B.
_________________

You've got what it takes, but it will take everything you've got

Senior SC Moderator
Joined: 22 May 2016
Posts: 1972
What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15  [#permalink]

### Show Tags

25 Sep 2017, 08:22
2
Gnpth wrote:
What is the Greatest Common Factor (GCF) of $$18x^8y^{(20)}$$ and $$24x^{(12)}y^{(15)}$$?

A. $$3x^4y^5$$

B. $$6x^4y^5$$

C. $$3x^8y^{(15)}$$

D. $$6x^8y^{(15)}$$

E. $$72x^{(12)}y^{(20)}$$

To find GCF, find the prime factorization of both expressions.

$$18x^8y^{(20)}$$ =
$$2 * 3 * 3 * x^8 * y^{(20)}$$

$$24x^{(12)}y^{(15)}$$ =
$$2 * 2 * 2 * 3 * x^{(12)} * y^{(15)}$$

Find all the factors they have in common, "to the lowest power."

Both expressions have 2 as a factor, for example, but the second expression has two more copies of 2. The first expression has only one copy of 2. Only one copy of 2 -- i.e., only one power of 2 -- can be counted towards the GCF.

For variables raised to powers, the lower power is the limiting factor used to find GCF.

Factors in common:

$$2 * 3 * x^8 * y^{(15)} =$$

$$6x^8y^{(15)}$$

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 278
Re: What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15  [#permalink]

### Show Tags

28 Sep 2017, 09:50
Gnpth wrote:
What is the Greatest Common Factor (GCF) of $$18x^8y^{(20)}$$ and $$24x^{(12)}y^{(15)}$$?

A. $$3x^4y^5$$

B. $$6x^4y^5$$

C. $$3x^8y^{(15)}$$

D. $$6x^8y^{(15)}$$

E. $$72x^{(12)}y^{(20)}$$

hi

the easiest way to solving this q

GCF of 18 and 24 is 6

now there are 8 xs and 12 xs
GCF will be 8 xs
because,

8*8*8*8*8*8*8*8*8*8*8*8
and
8*8*8*8*8*8*8*8

now you can clearly see that the highest number that can divide both is "x to the power 8"
the higher number above it cannot divide x^8
the lower number below it will divide both, but it cannot be highest common factor, as its name implies

in the same line of reasoning the GCF of y^15 and y^20 is y^15

cheers through the kudos button if this helps
Re: What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15 &nbs [#permalink] 28 Sep 2017, 09:50
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.