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Finding the Greatest Common Factor (GCF) - Lesson 2

This lesson focuses on finding the greatest common factor (GCF) of numbers, including using prime factors and algebraic expressions. Examples and practice problems included.

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Finding the Greatest Common Factor (GCF) - Lesson 2

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  1. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 2-5b Objective Find the greatest common factor (GCF) of two or more numbers

  4. Example 2-5b Vocabulary Venn diagram The use of circles to show how elements among sets of numbers or objects are related

  5. Example 2-5b Vocabulary Greatest common factor (GCF) The greatest of the common factors of two or more numbers

  6. Lesson 2 Contents Example 1Find the GCF by Listing Factors Example 2Find the GCF Using Prime Factors Example 3Find the GCF Using Prime Factors Example 4Find the GCF of an Algebraic Expression Example 5Use the GCF to Solve a Problem

  7. Example 2-1a Find the GCF of 28 and 42. Prime factor both 28 and 42 42 28 2 2 14 3 21 2 7 7 Circle factors that are common in each number then write the common factor Multiply the common factors 2  7 Answer: GCF = 14 14 Identify as GCF 1/5

  8. Example 2-1b Find the GCF of 18 and 45 Answer: GCF = 9 1/5

  9. Example 2-2a Find the GCF of 20 and 32. Prime factor both 20 and 32 20 32 2 2 2 10 2 16 2 8 5 4 2 2 Circle factors that are common in each number and write as factors Multiply the common factors 2  2 Answer: GCF = 4 4 Identify as GCF 2/5

  10. Example 2-2b Find the GCF of 24 and 36. Answer: GCF = 12 2/5

  11. Example 2-3a Find the GCF of 21, 42, and 63. Prime factor 21, 42 and 63 63 3 21 42 2 3 21 7 21 3 3 7 7 Circle factors that are common in each number and write as factors Multiply the common factors 3  7 Identify as GCF Answer: GCF = 21 21 3/5

  12. Example 2-3b Find the GCF of 24, 48, and 60. Answer: GCF = 12 3/5

  13. Example 2-4a ALGEBRAFind the GCF of 12p2 and 30p3 Prime factor 12p2 and 30p3 Multiply the common factors that are numbers 12p2 30p3 2 2 2 6p2 3 15p3 3p2 3 5p3 5 Multiply the common factors that are same variables p2 p p3 p p p2 p p Circle factors that are common in each number and write as factors 2  3  p  p Identify as GCF Answer: GCF = 6p2 6 6p2 4/5

  14. ALGEBRAFind the GCF of Example 2-4b Answer: GCF = 7mn 4/5

  15. Example 2-5a ARTCindy wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? Find the GCF of length of the tag board 15 3 25 5 5 5 There are no other common factors Circle factors that are common in each number and write as factors Identify as GCF GCF = 5 5 5/5

  16. Example 2-5a ARTCindy wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? GCF = 5 cm GCF = 5 Add dimensional analysis Answer: Cindy should use squares with sides measuring 5 centimeters 5/5

  17. Example 2-5b * CANDYAlice is making candy baskets using chocolate hearts and lollipops. She has 32 chocolate hearts and 48 lollipops. She wants to have an equal number of chocolate hearts and lollipops in each basket. Find the greatest number of chocolate hearts and lollipops Alice can put in each basket. Answer: 16 chocolate hearts and lollipops in each basket 5/5

  18. End of Lesson 2 Assignment

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