GCF


 * Greatest Common Factor (GCF) **

** Factoring out the GCF is number one priority when factoring. **

The GCF (Greatest Common Factor) is the highest number you can divide by for all the numbers. So, say if you had the numbers 4 and 12. The factors of 4 are: 1 and 4; and 2 and 2. The factors of 12 are: 1 and 12; 2 and 6; and 3 and 4. The GCF is 4 because both of these numbers greatest common factor between each is 4. After you find the GCF, you put it out front of your paranthesis. But remember, not every quadratic will have a GCF.

Let's try a few examples:

1) 4x 2 +10x+6

The first step is to find the GCF

Factors of 4:
 * 1 and 4
 * **2** and 2

Factors of 8:


 * 1 and 10
 * **2** and 5

Factors of 6:


 * 1 and 6
 * **2** and 3

After looking through, you notice that the greatest factor that all of them share is 2. So now you put it in front of your paranthesis. So now our problem would be 2(2x<span style="font-family: Arial,Helvetica,sans-serif; font-size: 70%; vertical-align: super;">2 +5x+3). Our final answer then would be 2(2x+3)(x+1)

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> __**Visual**__

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 4x 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">+10x+6 > **2**(4x 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">+10x+6) > __2(2x__ __<span style="font-family: Arial,Helvetica,sans-serif; font-size: 70%; vertical-align: super;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">+5x+3) __

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Let's do one more example:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">2) 12x 2 +8x-7

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Factors of 12:
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">1 and 12
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">2 and 6
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">3 and 4

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Factors of 8:
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">1 and 8
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">2 and 4

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Factors of 7:
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">1 and 7

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Now this is an example that there is no GCF in this quadratic equation. You might say "Well, all of them have a 1 in all of their factors." But we don't take out the 1 as a GCF because anything multiplied by 1 is still the same thing. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Our final answer; then, would be (6x-7)(2x-1).