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

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

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24 Sep 2017, 20:30
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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. $$72x^{(12)}y^{(20)}$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 24 Sep 2017, 20:40, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15 [#permalink]

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25 Sep 2017, 03:12
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.
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What is the Greatest Common Factor (GCF) of 18x^8y^(20) and 24x^12y^15 [#permalink]

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25 Sep 2017, 07:22
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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:

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

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

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

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28 Sep 2017, 08:50
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   [#permalink] 28 Sep 2017, 08:50
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