What is the GCF of #23x ^ { 4} ,x ^ { 2}#?

1 Answer
Apr 28, 2017

#x^2#

Explanation:

The Greatest Common Factor (GCF) is the largest term that can be found that is a factor of both of these terms.

Split it into two parts.
The GCF of the constants and the GCF of the variables.

Constants:

Our constants are #23# and #1#. Remember that there is a #1# in front of every number, we just don't write it because we know it's there.

So what is the largest number that fits into both #23# and #1#?
Well... #1#
So the GCF of our constants is #1#

Variables:

Our variables are #x^4# and #x^2#.This is the same thing. What is the largest variable that fits into both #x^4# and #x^2#?
That would be #x^2# because

#x^2(x^2)=x^4#

and

#x^2(1)=x^2#

We can't take more than #x^2# out of both of our variables.

So our GCF is the GCF of our constants times the GCF of our variables...

#1*x^2#

#1x^2#

But remember we already know there is a #1# next to every number, so there is no need to write it.

#x^2#