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
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
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
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 )