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