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

Question

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)}

pushpitkc · Answer

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.

generis · Answer

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

testcracker · Answer

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

Chethan92 · Answer

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.

pushpitkc · Answer

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)

niks18 · Answer

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

Abhishek009 · Answer

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)

Mo2men · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards