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Understanding the Greatest Common Factor (GCF): Methods and Applications

This lesson covers the concept of the Greatest Common Factor (GCF) and its importance in mathematics. Students will learn how to find the GCF of two or more numbers or monomials through two main methods. The lesson also includes practical applications, such as using the GCF to factor algebraic expressions with the distributive property. Examples will guide students to discover how the GCF applies to real-world situations, including distributing cookies into equal plates. Practice problems will reinforce these concepts to prepare students for mid-tests.

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Understanding the Greatest Common Factor (GCF): Methods and Applications

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  1. Lesson 4-4 Pages 164-168 Greatest Common Factor (GCF)

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

  3. Vocabulary

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

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

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

  7. Example 1: Method 1 Find the GCF of 16 and 24.

  8. Example 1: Method 2 Find the GCF of 16 and 24.

  9. Example 2: 7 Find the GCF of 28 and 35.

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

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

  12. 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?

  13. 2 x 3 x 5 = 30 GCF 30 plates

  14. Example 4: How many chocolate chip and molasses cookies will be on each plate?

  15. Example 5: Find the GCF: 2 • 3 • x • y • y = 6xy2

  16. 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)

  17. Page 167 Guided Practice #’s 4-16

  18. Read: Pages 164-166 with someone at home and study examples!

  19. Homework: Pages 167-168 #’s 18-54 even #’s 59-60, 67-81 Lesson Check 4-4

  20. Page 731 Lesson 4-4

  21. Lesson Check 4-4

  22. Prepare for Mid-Test! Pages 191-193 #’s 9-39 Odd Answers in Back of Book!

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