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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
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
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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 21 Aug 2018, 06:41
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Prime factorizing 18 and 24 gives
18 = 2*\(3^2\)
24 = \(2^3\)*3
GCF of 18 and 24 is 6
Again GCF of \(x^8\)\(y^{20}\) and \(x^{12}\)\(y^{15}\) is \(x^8\)\(y^{15}\)

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

D is the answer.
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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 21 Aug 2018, 06:43
Bunuel 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. \(72^{12}y^{20}\)


The greatest common factor of \(18x^8y^{20}\) and \(24x^{12}y^{15}\) can be found out as follows:

We can also write \(18x^8y^{20}\) as \(3*6*x^8*y^{15}*y^5\)
Similarly, we can write \(24x^{12}y^{15}\) as \(4*6*x^{8}*x^4*y^{15}\)

This follows the general rule of exponents which is \(a^{m+n} = a^m*a^n\)

Therefore, the greatest common factor(GCF) of \(18x^8y^{20}\) and \(24x^{12}y^{15}\) is \(6*x^8*y^{15}\)(Option 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 21 Aug 2018, 06:43
Bunuel 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. \(72^{12}y^{20}\)


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

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

Therefore \(GCD = 2*3x^8*y^{15}\), for GCD pick the lowest powers of \(x\) & \(y\)

Option 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 21 Aug 2018, 07:27
Bunuel 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. \(72^{12}y^{20}\)


Just find the common term only 10 sec required....

Common factor of \(18x^8y^{20}\) ,\(24x^{12}y^{15}\)

= \(6x^8y^{15} ( 3y^5 , 4x^4)\)

Thu, Answer must be (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 22 Aug 2018, 05:50
Bunuel 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. \(72^{12}y^{20}\)


GFC of 18 & 24 = 6.........Eliminate choices A, C & E

GFC of \(x^8\) and \(x^{12}\) = \(x^8\).....Eliminate B

Only one answer left

Answer: D
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Re: What is the Greatest Common Factor (GCF) of 18x^8y^20 and 24x^12y^15?   [#permalink] 22 Aug 2018, 05:50
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