Module 1 Lesson 1.6 - Factoring Part 3: GCF

Factoring Part 3: Two Methods for GCF

Module 1

Lesson 6

Start

Objectives:

• Find the Greatest Common Factor

Greatest Common Factor:

Factors:

a factor is one of the numbers or variables that are multiplied together to produce a product

What two numbers can you multiply together to get 12?

a common factor is any factor that two or more number share.

What factors do 12 and 18 have in common?

The Greatest Common Factor or (GCF) is the LARGEST factor two or more numbers share.

What is the GCF of 12 and 18: ____

Practice:

Find the GCF of 20 and 30 using the list method. Start with listing all of the factors of each:

Factors of 20: ____ x _____ , _____ x _____ , _____ x _____ Factors of 30: ____ x _____ , _____ x _____ , _____ x_____ Greatest Common Factor or GCF of 20 and 30: ______

these are all factors of 12!

What two numbers can you multiply together to get 18?

1 x 12

2 x 6

3 x 4

1 x 18

2 x 9

3 x 6

these are all factors of 18!

What about finding GCF for large numbers? The Ladder Method is probably more efficient! Find the LCM and GCF of 36 and 60 below:

Ladder Method for GCF:

Complete the 'Ladder' like we did for LCM by dividing by smaller factors like 2, 3, 5 or 7.Continue dividing until there are no common factors shared.

The LCM can be found by multiplying ALL numbers OUTSIDE the 'Ladder'. (Make an 'L' of the numbers).

The GCF can be found by multiplying just the VERTICAL numbers outside the 'Ladder'.

LCM of 36 and 60 =

GCF of 36 and 60 =

LCM of 45 and 60 =

GCF of 45 and 60 =

Practice:

Find the LCM and GCF of 45 and 60 below:

3 x 5 x 3 x 4 = 180

3 x 5 = 15

2 x 2 x 3 x 3 x 5 = 180

2 x 2 x 3 = 12