Greatest Common Factor

The Greatest Common Factor is the largest number that will divide into agroup of numbers

Examples:1.6, 92.15, 55

GCF = 3GCF = 5

3. What is the greatest common factor??

2436

GCF with Variables

Note: With variables, the GCF willAlways be the smallest exponent of aCommon variable

Examples:4.12x3, 16x2

5.45a5, 50a7

GCF = 4x2

GCF = 5a5

6. What is the greatest common factor??

5a2 35a

What is the greatest common factor??

9. -4x6 - x4 - 2x2 -x2

8. 22x2 – 11x

7. 3y -8xy

Factoring means to write as a product

Always look for a Greatest Common Factor 1st.

Factor 4x + 6y What is their greatest

common factor?

= 2( )2x

+ 3yLets check.

=2(2x+3y) = 4x+6y

11. 3y – 8xy

FactorWhat is their

GCF?

= y( )3– 8x

12. 2a3 – 6ab2

= 2a( )a2 – 3b2

13. 2h2k + 2kFactor

What is their GCF?

= 2k( )h2+ 1

14. 6uv + 9v2

= 3v( )2u

+ 3v

What if there is not GCF?

3x + 2

x2 + 3x + 2

Then it is prime

Unless it is a trinomial, then I have to use another method.

GCF• Factor:• xy – 5y• What is common?• Answer: y(x - 5)• What if we change the expression slightly?• x(x + 4) – 5(x + 4)• What is common?• Answer: (x + 4)(x – 5 )

GCF

• Try these:

• 3x2 – 6x – 15x3

• 16x2 – 8x

• y(y – 6) + 9(y – 6)