Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, 9 2.15, 55 GCF = 3 GCF.

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Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF = 5

3. What is the greatest common factor?? 24 36

GCF with Variables Note: With variables, the GCF will Always be the smallest exponent of a Common variable Examples: 4.12x 3, 16x a 5, 50a 7 GCF = 4x 2 GCF = 5a 5

6. What is the greatest common factor?? 5a 2 35a

What is the greatest common factor?? 9. -4x 6 - x 4 - 2x 2 -x x 2 – 11x 7. 3y -8xy

Factoring means to write as a product Always look for a Greatest Common Factor 1 st. Factor 4x + 6y What is their greatest common factor? = 2( ) 2x + 3y Lets check. =2(2x+3y) = 4x+6y

11.3y – 8xy Factor What is their GCF? = y( ) 3 – 8x 12. 2a 3 – 6ab 2 = 2a( ) a2a2 – 3b 2

13. 2h 2 k + 2k Factor What is their GCF? = 2k( ) h2h uv + 9v 2 = 3v( ) 2u + 3v

What if there is not GCF? 3x + 2 x 2 + 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: 3x 2 – 6x – 15x 3 16x 2 – 8x y(y – 6) + 9(y – 6)