Question

What is the greatest common factor of 20x4 and 6x3?
A. x3
B. x4
C. 2x3
D. 2x4

Answer 1

Look at the numbers first: 20 and 6.
What is their GCF?

Answer 2

is it 2 ?

Answer 3

20 = 2 * 2 * 5
6 = 2 * 3
The only factor they have in common is 2.

Answer 4

at least i was right , what's next ?

Answer 5

Correct.
Now look at the variable parts: x^4 and x^3.
x^4 = x * x * x * x
x^3 = x * x * x
How many x's do they have in common?

Answer 6

if were counting the x in front of the number's then they have 4 in common but if not they only have 3 in common .

Answer 7

No.
It's true that the first one has 4 x's and the second one has 3 x's.
How many they have in common means the _highest_ number of x's they both have. They both have 3 x's, but they both don't have 4, so they have 3 x's in common. That means they have x^3 in common.

Answer 8

so the answer is x^3

Answer 9

Yes, for the variables in common

Now you put together both parts (the number in common and the variables in common)to form your answer:
The two given terms have 2 in common and x^3 in common.
The GCF is 2x^3