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Lesson 4.2 Greatest Common Factor

Lesson 4.2 Greatest Common Factor . Essential Question: How do you find the greatest common factor of two or more numbers?. Before we start…. What does it mean to have something in common? What do the numbers 4 and 8 have in common?. What is a factor?.

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Lesson 4.2 Greatest Common Factor

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  1. Lesson 4.2Greatest Common Factor Essential Question: How do you find the greatest common factor of two or more numbers?

  2. Before we start… What does it mean to have something in common? What do the numbers 4 and 8 have in common?

  3. What is a factor? • Remember a factor is any whole number that can be divided exactly into another number. • 1, 2, 3, and 6 are factors of 6.

  4. What is a common factor? • A common factor is a whole number that is a factor of two or more nonzero whole numbers. • 3 is a common factor of 3, 6, 9 and 12.

  5. What is the greatest common factor (GCF)? • The greatest common factor (GCF) is the greatest of the common factors. • It’s the highest number factor that appears in each number’s factor list. • 12 has the factors: 1, 2, 3, 4, 6 and 12. • 16 has the factors: 1, 2, 4, 8 and 16. • The GCF of 12 and 16 would be 4.

  6. How do you find a GCF? • Make a list of all the factors and identify the greatest number on each list. • Write the prime factorization of each number. • Find the common prime factors. • Multiply the factors. Your product is the GCF.

  7. Find the greatest common factor of 56 and 84.

  8. Find the greatest common factor of 12 and 32.

  9. Find the greatest common factor of 42 and 60.

  10. Find the greatest common factor of 22 and 38.

  11. Find the greatest common factor of 36 and 90.

  12. Find the greatest common factor of 14 and 70.

  13. Find the greatest common factor of 180 and 126.

  14. Find the greatest common factor of 3, 9 and 27.

  15. Find the greatest common factor of 21, 28 and 56.

  16. What if there isn’t any GCF? • Sometimes you’ll have numbers that won’t have any factor in common other than 1. • Two numbers are relatively prime if their greatest common factor is 1. • 8 and 15 are relatively prime.

  17. Tell whether the numbers 112 and 45 are relatively prime.

  18. Tell whether the numbers 9 and 20 are relatively prime.

  19. Tell whether the numbers 10 and 25 are relatively prime.

  20. Tell whether the numbers 5 and 16 are relatively prime.

  21. Orchestra An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the same number of each instrument. What is the greatest number of ensembles that can be formed? How many violinists, violists, and cellists will be in each ensemble?

  22. Pep Rally Students at your school are planning to hand out pep rally packs to support your school’s athletic program. The students have 240 bumper stickers, 360 pennants, and 720 pencils. Every pack must have the same contents, and no items should be left over. What is the greatest number of packs that can be made? What will each pack contain?

  23. Snacks Elisha and David are putting together snack packs for a large group of hikers. They have 160 apples, 320 carrot sticks, and 400 celery sticks. Each snack pack has the same contents and there are no leftover items. What is the greatest number of snack packs that can be made and what is in each pack?

  24. Soccer Teams In a youth sports league, 60 girls and 66 boys will be divided into teams. Each team will have an equal number of players and will have the same number of girls. What is the greatest number of teams that can be formed?

  25. How do you find the greatest common factor of two or more numbers?

  26. Ticket Out the Door Find the greatest common factor of 16 and 28

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