Question

Will someone please help me with GCF? @satellite73

Answer 1

of what?

Answer 2

well, this is the first question idk how to do-
"Find the GCF of the following literal terms:
m^7 n^4 p^3 and mn^12 o^5"

Answer 3

i meant p^5 for the last one

Answer 4

i take it you mean \(m^7 n^4 p^3\) and \(mn^{12}p^5\)

Answer 5

Yes, I just don't know how to type it so that it shows up like that. But yes that is what I meant.

Answer 6

take each factor you see to the LOWEST power you see it

Answer 7

Does that mean if I see m to the 7th power I'm supposed to change it to m to the first power?

Answer 8

\[gcf(m^7 \cdot n^4 \cdot p^3 , m^1 \cdot n^{12} \cdot p^5 )=m^{\min(7,1)} \cdot n^{\min(4,12)} \cdot p^{\min(3,5)}\]

where the min(a,b) means find the smaller of a and b and that is your power for that variable.

Answer 9

no, the lowest one, not the highest
you have \(m^7\) in one term, but only \(m^1\) in the second,
only use \(m^1\) or just \(m\)

Answer 10

\(\bf (m^7 n^4 p^3) ( mn^{12} o^5)\implies ({\color{red}{ m^1}}\cdot m^6 {\color{red}{ n^4}} p^3) ( {\color{red}{ m^1n^4}}\cdot n^{8} o^5)\)

Answer 11

thank you I understand!
but how do you do it when the powers aren't listed-
"xxyyyzz and xxxxzzz"

Answer 12

you split them up

Answer 13

What does that mean

Answer 14

You can also look at it like this:
\[\gcd(x^2 y^3 z^2, x^4 y^0 z^3)=x^{\min(2,4)} y^{\min(3,0)}z^{\min(2,3)}\]

Answer 15

\(\bf a^{\color{red}{ n}}\cdot a^{\color{red}{ m}}\cdot a^{\color{red}{ z}}\implies a^{{\color{red}{ n+m+z}}}
\\ \quad \\
a^{25}\implies a^{10+10+5}\implies a^{10}a^{10}a^5\)

Answer 16

do you know what the min(2,4)=?

(in other words, which is smaller 2 or 4?)

Answer 17

^ 2 is smaller

Answer 18

\[\gcd(x^2 y^3 z^2, x^4 y^0 z^3)=\]
\[x^{\min(2,4)} y^{\min(3,0)}z^{\min(2,3)}=\gcd(x^2 y^3 z^2, x^4 y^0 z^3)=x^2 y^{\min(3,0)}z^{\min(2,3)}\]
So see I replace the min(2,4) with 2

Answer 19

you try the rest

Answer 20

Thank you so much everyone who is helping!!
And okay since the lowest for y is 0 there is no y in the answer and since the lowest for both x and z is 2 the answer should be
\[x ^{2}y ^{2}\]

Answer 21

you meant that y to be a z right?

Answer 22

oh yeah oops. I meant x squared z squared because there is no y since the lowest was 0

Answer 23

greatness

Answer 24

Yay!! Thank you! I have one last question. Can you please tell me if I worked this problem correctly?
\[8x ^{6}y ^{5} - 3x ^{8}y ^{3}\]

so I was gonna say the lowest between the numbers is 3, the lowest factor of x is 6, and the lowest factor of y is 2.

but I'm confused because it says to subtract.

Answer 25

i meant to lowest of y is 3

Answer 26

yes

Answer 27

how do I write it out as an answer though

Answer 28

\(\bf 8x ^{6}y ^{5} - 3x ^{8}y ^{3}\implies 8{\color{red}{ x^{6}}}{\color{red}{ y^3}}y ^{2} - 3x^2\cdot {\color{red}{ x^{6}y ^{3}}}\)

Answer 29

take the GCF out and leave everything else there

Answer 30

Okay thank you so much.

Answer 31

yw