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Find Common Factors and Greatest Common Factor

Learn how to find common factors and the greatest common factor (GCF) of a set of whole numbers in this lesson.

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Find Common Factors and Greatest Common Factor

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 8–7) Main Idea and Vocabulary Example 1: Find Common Factors Example 2: Numbers with One Common Factor Example 3: Find the Greatest Common Factor Example 4: Use the Greatest Common Factor Lesson Menu

  3. I will identify common factors of a set of whole numbers. • common factor • greatest common factor (GCF) Main Idea/Vocabulary

  4. Find Common Factors Find the common factors of 12 and 18. Step 1 List all the factors of each number. 12 = 1 × 12 12 = 2 × 6 12 = 3 × 4 factors of 12: 1, 2, 3, 4, 6, 12 18 = 1 × 18 18 = 2 × 9 18 = 3 × 6 factors of 18: 1, 2, 3, 6, 9, 18 Example 1

  5. Find Common Factors Step 2 Find the common factors. factors of 12: 1, 2, 3, 4, 6, 12 factors of 18: 1, 2, 3, 6, 9, 18 Answer: The common factors are 1, 2, 3, and 6. Example 1

  6. A B C D Which lists the common factors of 15 and 21? • 1, 3 • 1, 2, 3 • 1, 3, 5 • 1, 3, 5, 7 Example 1

  7. Numbers with One Common Factor Find the common factors of 8, 14, and 21. factors of 8: 1, 2, 4, 8 factors of 14: 1, 2, 7, 14 factors of 21: 1, 3, 7, 21 Answer: The only factor common to all three numbers is 1. Example 2

  8. A B C D Find the common factors of 6, 15, and 23. • 1, 2, 3, 6 • 1, 3, 5 • 1, 3 • 1 Example 2

  9. Find the Greatest Common Factor Find the greatest common factor of 12, 16, and 18. List all of the factors of 12, 16, and 18 to find the common factors. factors of 12: 1, 2, 3, 4, 6, 12 factors of 16: 1, 2, 4, 8, 16 factors of 18: 1, 2, 3, 6, 9, 18 The common factors are 1 and 2. The greatest of these is 2. Example 3

  10. Find the Greatest Common Factor Answer: So, the greatest common factor, or GCF, of 12, 16, and 18 is 2. Example 3

  11. A B C D Find the greatest common factor of 5, 15, and 25. • 2 • 3 • 4 • 5 Example 3

  12. Use the Greatest Common Factor Olimpia is making a vegetable platter using 32 tomato slices and 48 cucumber slices. She wants to put an equal number of tomato slices and an equal number of cucumber slices on each plate. What is the greatest number of plates she can make? First, find the common factors of each number. factors of 32: 1, 2, 4, 8, 16, 32 factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 common factors of 32 and 48: 1, 2, 4, 8, 16 Example 4

  13. Use the Greatest Common Factor Olimpia can make 1, 2, 4, 8, or 16 plates with each plate having an equal number of tomato slices and an equal number of cucumber slices. Answer: Since 16 is the GCF, the greatest number of plates Olimpia can make is 16. Check There will be 32 ÷ 16, or 2 tomato slices and 48 ÷ 16 or 3 cucumber slices on each plate. Example 4

  14. A B C D Serena is making two appetizers for her party. She has 48 mini meatballs and 56 crackers with cheese. She wants to put the same number of appetizers on each serving plate. What is the greatest number of plates she can make? • 1 plate • 4 plates • 8 plates • 12 plates Example 4

  15. End of the Lesson End Lesson

  16. Five-Minute Check (over Lesson 8–7) Image Bank Math Tool Chest Compare Fractions Resources

  17. A B C D (over Lesson 8–7) Use any strategy to solve. Jake went to see a play at his high school. It started at 6:35 P.M. and lasted 1 hour and 55 minutes. At what time did the play end? • 9:25 A.M. • 8:30 P.M. • 8:45 P.M. • 7:00 P.M. Five Minute Check 1

  18. End of Custom Shows

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