Question

Find the GCF.


A. 28a3b3c4
The three's and the four are small here.
B. 14

C. 14abc

D. 28abc

Answer 1

The equation is above.

Answer 2

can you find the GCF for 14 and 28?

Answer 3

GCF is the biggest number that divides evenly into both.

Answer 4

7? @phi

Answer 5

7 is a common factor, but not the biggest. how about 14?

Answer 6

14 divides into 14 and into 28 evenly, right?

Answer 7

That would work!

Answer 8

so 14 is part of the answer.

any idea what the GCF is for
a and a*a
?

Answer 9

That's where I get lost! lol

Answer 10

with a letter you don't have a lot of options. the only thing we know that will divide evenly into "a" is itself.

Answer 11

and what is A. standing for?

Answer 12

a is a number. But we know this: a/a = 1 (anything divided by itself is 1)
which means a divides evenly into a.
The next question is , does a divide evenly into a*a ?

Answer 13

Yeah I think it would.

Answer 14

you can re-write it like this
\[ \frac{a\cdot a}{a} = \frac{a}{a} \cdot a\]
now use a/a= 1 to say
\[ 1 \cdot a = a \]
in other words, a*a/a = a with NO remainder. (i.e. divides evenly)

so a divides evenly into a and into a*a

and because there is no other thing (except 1) that divides into a (as far as we know), a is the greatest common factor of a and a*a

Answer 15

btw,
\[ a \cdot a= a^2\]
so we found the GCF of \( a \text{ and } a^2\)

Answer 16

so far the GCF is 14a

any idea what the GCF of b and b*b is ?

Answer 17

7?

Answer 18

the gcf of a letter b and b*b is not a fixed number. It will be a letter

Answer 19

b?

Answer 20

LOL Im sorry... I'm horible at these thing's.

Answer 21

yes, b is the only thing other than 1 that evenly divides into both b and b*b

Answer 22

YAY!

Answer 23

If you are lost, it's because there is an idea you are missing. Once you get the idea, it makes sense.

Answer 24

now the gcf of c and c*c*c ?

Answer 25

C.!

Answer 26

Option C. is looking promising...

Answer 27

yes, and all together we get
14abc

Answer 28

WOW!! Thanks for working with me man! I really appreciate it!!

Answer 29

*handshake*

Answer 30

if you have the idea, then what is the gcf of
a*a and a*a*a
?
any idea ?

Answer 31

A.!

Answer 32

a is a factor, but we can do more.

Answer 33

A and A???

Answer 34

\[ \frac{a\cdot a}{a\cdot a} = \frac{a}{a} \cdot \frac{a}{a} = 1\]
in other words
a*a divides evenly into a*a

Answer 35

yes, but I would say A TIMES A (not A and A)

Answer 36

OOOOhhh alright! Cool!

Answer 37

and \[ \frac{a\cdot a\cdot a}{a\cdot a} = a \]

so a*a is the gcf of a*a and a*a*a

Answer 38

or, using exponents
the gcf of \( a^2 \) and \(a^3\) is \( a^2 \)

Answer 39

Okay! Wow. Thanks again for all your brainpower! =)