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Greatest Common Factor

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This guide explains the concept of the greatest common factor (GCF) of numbers and how to find it. Factors are numbers that divide evenly into another, and the GCF is the largest factor shared between two or more numbers. The document provides examples of finding factors for various numbers and identifies common factors among them. Additionally, it describes how to simplify fractions using the GCF to achieve their simplest form. This understanding is crucial for various mathematical operations and enhances number sense.

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Greatest Common Factor

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  1. Greatest Common Factor By Monica Yuskaitis

  2. Factor • A number that divides evenly into another. • Factors of 24 are 1,2, 3, 4, 6, 8, 12 and 24.

  3. What are the factors of 9? • Factors of 9 are 1, 3 and 9.

  4. What are the factors of 10? • Factors of 10 are 1, 2, 5 and 10.

  5. What are the factors of 7? • Factors of 7 are 1 and 7.

  6. What are the factors of 56? • Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

  7. Common Factor • When two numbers have the same factor it is called a common factor. • A common factor of 12 and 6 is 3.

  8. Name a Common Factor of 9 and 27? 1, 3, 9

  9. Name a Common Factor of 4 and 8? 1, 2, 4

  10. Name a Common Factor of 4 and 8? 1, 2, 4

  11. Name a Common Factor of 15 and 30? 1, 3, 5, 15

  12. Name a Common Factor of 12 and 48? 1, 2, 3, 4, 6, 12

  13. Name a Common Factor of 7 and 21? 1, 7

  14. Name a Common Factor of 10 and 30? 1, 5, 10

  15. Name a Common Factor of 3 and 4? 1

  16. Simplest Form • When the only common factor of the numerator and denominator is 1, the fraction is in simplest form. 3 1 3 ÷ = 4 1 4

  17. Greatest Common Factor • The greatest common factor is the largest factor between two numbers. 12 = 1, 2, 3, 4, 6, 12 18 = 1, 2, 3, 6, 9, 18

  18. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 12 = 1, 2, 3, 4, 6, 12

  19. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 14 = 1, 2, 7,14

  20. What is the Greatest Common Factor? 6 = 1, 2, 3, 6 18 = 1, 2, 3, 6, 9, 15

  21. What is the Greatest Common Factor? 6 = 1, 2, 3, 6 12 = 1, 2, 3, 4, 6, 12

  22. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 16 = 1, 2, 4, 8, 16

  23. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 10 = 1, 2, 5, 10

  24. What is the Greatest Common Factor? 3 = 1, 3 6 = 1, 2, 3, 6

  25. What is the Greatest Common Factor? 4 = 1, 2, 4 6 = 1, 2, 3, 6

  26. What is the Greatest Common Factor? 7 = 1, 7, 21 = 1, 3, 7, 21

  27. What is the Greatest Common Factor? 15 = 1, 3, 5, 15 24 = 1, 2, 3, 8, 12, 24

  28. How to Find the Simplest Form of a Fraction • Find the greatest common factor of the numerator and the denominator and divide both the numerator and the denominator by that number. 12 6 2 ÷ = 18 6 3

  29. Simplify or Reduce This Fraction 12 6 2 ÷ = 18 6 3

  30. Simplify or Reduce This Fraction 9 3 3 ÷ = 21 3 7

  31. Simplify or Reduce This Fraction 12 4 3 ÷ = 20 4 5

  32. Simplify or Reduce This Fraction 10 5 2 ÷ = 15 5 3

  33. Simplify or Reduce This Fraction 10 2 5 ÷ = 16 2 8

  34. Simplify or Reduce This Fraction 12 4 3 ÷ = 16 4 4

  35. Simplify or Reduce This Fraction 3 3 1 ÷ = 12 3 4

  36. Simplify or Reduce This Fraction 2 2 1 ÷ = 8 2 4

  37. Simplify or Reduce This Fraction 2 2 1 ÷ = 4 2 2

  38. Simplify or Reduce This Fraction 6 3 2 ÷ = 9 3 3

  39. Simplify or Reduce This Fraction 6 2 3 ÷ = 8 2 4

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