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

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

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

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

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

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

Example 2-1a Find the GCF of 28 and 42. Prime factor both 28 and 42 28 42 2 14 2 7 2 213 7 Circle factors that are common in each number then write the common factor 2  7 14 1/5 Multiply the common factors Identify as GCF Answer: GCF = 14

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

Example 2-2a Find the GCF of 20 and 32. Answer: GCF = 4 Prime factor both 20 and 32 2032 2 10 2 5 2 162 82 2 4 2 Circle factors that are common in each number and write as factors 2  2 4 2/5 Multiply the common factors Identify as GCF

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

Example 2-3a Find the GCF of 21, 42, and 63. Answer: GCF = 21 Prime factor 21, 42 and 63 2142 63 3 7 2 21 3 7 3 3 7 3  7 3/5 Circle factors that are common in each number and write as factors Multiply the common factors 21 Identify as GCF

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

Example 2-4a ALGEBRA Find the GCF of 12p 2 and 30p 3 Answer: GCF = 6p 2 Prime factor 12p 2 and 30p 3 12p 2 30p 3 2 6p 2 3p 2 p2p2 p 2 3 p 2 15p 3 3 5p 3 5 p3p3 p p2p2 p p 2  3  p  p 6p 2 4/5 Circle factors that are common in each number and write as factors 6 Multiply the common factors that are numbers Multiply the common factors that are same variables Identify as GCF

Example 2-4b ALGEBRA Find the GCF of Answer: GCF = 7mn 4/5

Example 2-5a ART Cindy 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 15 253 5 5 5 There are no other common factors 5/5 Circle factors that are common in each number and write as factors 5 Identify as GCF GCF = 5

Example 2-5a ART Cindy 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? Answer: Cindy should use squares with sides measuring 5 centimeters 5/5 GCF = 5 Add dimensional analysis GCF = 5 cm

Example 2-5b CANDY Alice 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

End of Lesson 2 Assignment Lesson 5:2 Greatest Common Factor 9 - 29 All

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