Lesson 4-4 Pages Greatest Common Factor (GCF)

What you will learn! 1. How to find the GCF of two or more numbers or monomials. 2. How to use the distributive property to factor algebraic expressions.

Greatest common factor

What you really need to know! The greatest number that is a factor of two or more numbers is the greatest common factor (GCF).

What you really need to know! In algebra, greatest common factors are used to factor expressions.

What you really need to know! There are two main methods for finding the GCF.

Example 1: Method 1 Find the GCF of 16 and x 16 1 x 24 2 x 8 2 x 12 4 x 4 3 x 8 4 x 6 Common Factors GCF8

Example 1: Method 2 Find the GCF of 16 and = 2 x 2 x 2 x 2 24 = 2 x 2 x 2 x 3 2 x 2 x 2 = 8 GCF

Example 2: Find the GCF of 28 and = 2 x 2 x 7 35 = 5 x 7 5 x 7 7

Example 3: Find the GCF of 12, 48 and = 2 x 2 x 3 48 = 2 x 2 x 2 x 2 x 3 72 = 2 x 2 x 2 x 3 x 3 2 x 2 x 3 = 12 GCF

Example 4: Parents donated 150 chocolate chip cookies and 120 molasses cookies for a school bake sale.

Example 4: If the cookies are arranged on plates, and each plate has the same number of chocolate chip cookies and each plate has the same number of molasses cookies, what is the largest number of plates possible?

120 = 2 x 2 x 2 x 3 x = 2 x 3 x 5 x 5 2 x 3 x 5 = 30 GCF 30 plates

Example 4: How many chocolate chip and molasses cookies will be on each plate? 150 ÷ 30 = 5 Chocolate chip 120 ÷ 30 = 4 Molasses

Example 5: 18x 3 y 2 = x x x y y 42xy 2 = x y y 2 3 x y y = 6xy 2 Find the GCF:

Example 6: Factor: 3x + 12 Since 3 and 12 are both divisible by 3, you can use the distributive property to rewrite the expression as 3(x + 4)

Page 167 Guided Practice #’s 4-16

Pages with someone at home and study examples! Read:

Homework: Pages #’s even #’s 59-60, Lesson Check 4-4

Page 731 Lesson 4-4

Lesson Check 4-4

Prepare for Mid-Test! Pages #’s 9-39 Odd Answers in Back of Book!