Question

Find the greatest common factor of these two expressions.

27x^5 v^2 u^6 and 18w^4 v^7

I think the answer is 9^2

Any help? Please?

Answer 1

But not every variable has a 9 or greater...

Answer 2

oh oops I meant 3^2 ...3 cann go into 27 and 18

Answer 3

\[27x^5v^2u^6\]\[18w^4v^7\]

can't you factor out a 9 from both? How about \(v^2\)?

Answer 4

But not every variable has 3 either...

Answer 5

hmmm ok...can you teach me? I want to learn how to do this :)

Answer 6

For example v^2 has a GCF of 1 because it's not 2v^2 or 3v^2

Answer 7

Ok, that makes sense

Answer 8

write each expression as its prime factors:

\[27x^5v^2u^6 = 3*3*3*x*x*x*x*x*v*v*u*u*u*u*u*u = 3^3x^5v^2u^6\]
\[18w^4v^7 = 2*3*3*w*w*w*w*v*v*v*v*v*v*v = 2^13^2w^4v^7\]

the GCF is the highest common power of any factor found in both:

GCF = \(3^2v^2 = 9v^2 \)

Answer 9

You can factor \(3^2v^2\) out of both expressions:

\[27x^5v^2u^6 = 9v^2(3x^5u^6)\]\[18w^4v^7 = 9v^2(2w^4v^5)\]

there are no additional common factors which can be taken out after doing so, so \(9v^2\) is the GCF

Answer 10

ohhh so I was close...just missing the v?

Answer 11

yes, I wondered if that was a typo or a braino :-)

Answer 12

Braino, I did half of the steps right...pffff always good to doubel check, I'm doing a review before I take the actual test.

Answer 13

well, another way to think of this is to first find the GCF of the coefficients:

GCF of 18 and 27 is obviously 9, right?

Then find the GCF of the variables (should be pretty clear that is \(v^2\) here, I hope!)

Multiply the GCF of variables and GCF of coefficients together to get the complete GCF

Answer 14

ooooh thank you! all these neat tips and tricks :)