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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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New post Updated on: 24 Sep 2017, 21:40
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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. \(72x^{(12)}y^{(20)}\)

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

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New post 25 Sep 2017, 08:22
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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:

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

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

Answer D
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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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New post 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

Answer:D

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