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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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21 Aug 2018, 05:36
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25% (medium)

Question Stats:

74% (00:50) correct 26% (00:39) wrong based on 57 sessions

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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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21 Aug 2018, 05:41
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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21 Aug 2018, 05:43
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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21 Aug 2018, 05:43
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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21 Aug 2018, 06:27
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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22 Aug 2018, 04:50
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

Re: What is the Greatest Common Factor (GCF) of 18x^8y^20 and 24x^12y^15? &nbs [#permalink] 22 Aug 2018, 04:50
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# What is the Greatest Common Factor (GCF) of 18x^8y^20 and 24x^12y^15?

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