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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 21 Aug 2018, 06:36
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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. \(72^{12}y^{20}\)

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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
1
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
Re: What is the Greatest Common Factor (GCF) of 18x^8y^20 and 24x^12y^15? &nbs [#permalink] 22 Aug 2018, 05:50
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