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

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Question Stats: 79% (01:10) correct 21% (01:21) wrong based on 126 sessions

### HideShow timer Statistics 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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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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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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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

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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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1
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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$$x^8$$$$y^{15}$$

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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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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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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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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 $$18x^8y^{20}$$ ,$$24x^{12}y^{15}$$

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

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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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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 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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