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Factor Out The Greatest Common Factor (GCF)

Learn how to factor out the greatest common factor (GCF).

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In this video, we are going to look at how to factor out the greatest common factor.
For example:
To factor:
x^2+5x
we can factor out a variable, x, by dividing it out of each term, leaving us with
x(x+5)
To factor:
3y^4+6y^3+12y^2
the largest number we can pull out from all of the terms is 3, and the largest variable is y^2. So if we factor out 3y^2 then we would be left with
3y^2(y^2+2y+4)
To factor:
8x^3y^2+24x^4y-20x^2y^2
the largest number that can be pulled out is 4, the largest variable in terms of x is x^2, and the largest variable in terms of y is just y. So if we factor out 4x^2ythen we would be left with
4x^2y(2xy+6x^2-5y)

Factor Out the Greatest Common Factor (GCF)

Video-Lesson Transcript

Let’s go over factoring out the greatest common factor.

We have this expression:

x^2 + 5x

We may need to factor this.

The coefficients are 1 and 5.

The greatest common factor of these two is 1.

But it will not help us. Since when we divided by 1, we have the same exact expression.

But we can factor out the variable x. Both terms can be divided by x.

So, we’re taking x out.

When we factor, we divide out whatever the greatest common factor is.

Factoring undoes multiplication.

So when we find the greatest common factor, we divide it out in each term.

So in x^2 + 5x,

let’s take x out.

Our answer is x (x + 5).

We could see if we’re actually multiplying this. If we end up with the original expression.

Let’s distribute x into each term in the parenthesis.

x (x + 5)
x^2 + 5x

Let’s look at a more complex example

3y^4 + 6y^3 + 12y^2

First, let’s figure out what the greatest common factor is of the coefficients.

So, 3, 6, and 12.

The biggest number that goes into all of them is 3.

Here’s a trick:

The greatest common factor of the variable is the term with the lowest exponent.

So in this case, y^2 is the greatest common factor of the variable. So let’s take it out.

Now, let’s divide each term by 3y^2.

3y^4 + 6y^3 + 12y^2
3y^2 (y^2 + 2y + 4)

Let’s try an even more complicated example

8x^3y^2 + 24 x^4y - 20x^2y^2

What’s the greatest common factor of 8, 24 and 20?

4.

What about the smallest exponent?

x^2 and y

Now let’s divide 8x^3y^2 + 24 x^4y - 20x^2y^2 by it’s greatest common factor 4x^2y

4x^2y (2xy + 6x^2 - 5y)

To recap, when factoring out the greatest common factor, we have to find the greatest common factor of each of the coefficients. And find what variables are in common with the smallest exponent.

And divide each term by the greatest common factor.

We’ll have a monomial and polynomial.

The monomial being the greatest common factor or GCF.