Question

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

Answer 1

`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`