1 / 30

Factorization

Factorization. Greatest Common Factor Least Common Multiple. Why Factor?. Factors allow you to break composite numbers down to their component parts. Factors are used to simplify fractions. Factors are used to identify the greatest common factor (GCF) and the least common multiple (LCM).

rhian
Download Presentation

Factorization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Factorization Greatest Common Factor Least Common Multiple

  2. Why Factor? • Factors allow you to break composite numbers down to their component parts. • Factors are used to simplify fractions. • Factors are used to identify the greatest common factor (GCF) and the least common multiple (LCM). • A number can be written as the product of its prime factors.

  3. Find Factor Pairs for 24 • Start with 1: 1 x 24 = 24 • 2: 2 x 12 = 24 • 3: 3 x 8 = 24 • 4: 4 x 6 = 24 • 6: 6 x 4 = 24 • 8: 8 x 3 = 24 • 12: 12 x 2 = 24 • 24: 24 x 1 = 24 The commutative property shows the same pairs: 1 x 24 = 24 x 1 2 x 12 = 12 x 2 3 x 8 = 8 x 3 4 x 6 = 6 x 4

  4. Prime Factorization • Prime numbers are numbers that have only one and the number as factors. • “1” is neither prime or composite. • Composite numbers can be written as products of their prime factors.

  5. Factorization Upside Down Division

  6. Prime factorization of 24 2 24 2 12 2 6 3 Prime Factorization is 2 x 2 x 2 x 3

  7. Prime factorization of 28 2 28 2 14 7 Prime Factorization is 2 x 2 x 7

  8. Prime factorization of 15 3 15 5 Prime Factorization is 3 x 5

  9. Prime factor 40 2 40 2 20 2 10 5 Prime Factorization is 2 x 2 x 2 x 5

  10. Greatest Common Factor (GCF) • Definition: • The largest factor that divides evenly into 2 or more numbers. • Examples: • 3 and 7 have no common factors other than 1 • 4 and 6 have the greatest common factor of 2 • 6 and 24 have a greatest common factor of 6 • 10 and 15 have a GCF of 5

  11. Greatest Common Factor Use Factorization

  12. Prime factor 28 and 16 to find the GCF 2 28 2 14 7 Prime Factorization of 28: 2 x 2 x 7 2 16 2 8 2 4 2 Prime Factorization of 16: 2 x 2 x 2 x 2

  13. Prime factor 28 and 16 2 28 2 14 7 Prime Factorization of 28: 2 x 2 x 7 2 16 2 8 2 4 2 Prime Factorization of 16: 2 x 2 x 2 x 2 GCF is 2 x 2 = 4

  14. Factor both numbers 28 and 16 at the same time 2 28 16 2 14 8 7 4 The GCF is the product of the common prime factors: 2 x 2 = 4

  15. Factor both numbers: 24 and 30 2 24 30 3 12 15 4 5 The GCF is the product of the common prime factors: 2 x 3 = 6

  16. Factor both numbers: 28 and 42 G • 2 28 42 • 14 21 • 2 3 • The GCF is the product of the common prime factors: 2 x 7 = 14

  17. Factor both numbers: 12 and 30 G 2 12 30 3 6 15 2 5 The GCF is the product of the common prime factors: 2 x 3 = 6

  18. Least Common Multiple Use Factorization

  19. Factor both numbers 28 and 16 at the same time 2 28 16 2 14 8 7 4 The LCM is the product of ALL the factors: 2 x 2 x 7 x 4 = 112

  20. Factor both numbers: 24 and 30 2 24 30 3 12 15 4 5 The LCM is the product of ALL of the factors: 2 x 3 x 4 x 5 = 120

  21. Factor both numbers: 28 and 42 • 2 28 42 • 14 21 • 2 3 • The LCM is the product of ALL of the factors: 2 x 7 x 2 x 3 = 84

  22. Factor both numbers: 12 and 30 2 12 30 3 6 15 2 5 The LCM is the product of ALL of the factors: 2 x 3 x 2 x 5 = 60

  23. Greatest Common Factor and Least Common Multiple

  24. Factor both numbers: 10 and 30 G 5 10 30 2 2 6 1 3 GCF: 5 x 2 = 10 LCM: 5 x 2 x 1 x 3 = 30

  25. Factor both numbers: 12 and 40 G 2 12 40 2 6 20 3 10 GCF: 2 x 2 = 4 LCM: 2 x 2 x 3 x 10 = 120

  26. Factor both numbers: 12 and 40 G 2 12 40 2 6 20 3 10 GCF: 2 x 2 = 4 LCM: 2 x 2 x 3 x 10 = 120

  27. Simplifying Fractions Greatest Common Factor

  28. Simplify 24/30 2 24 30 3 12 15 4 5 The fraction 24/30 simplifies to 4/5 (The GCF was used: 24/6 = 4, 30/6 = 5)

  29. Simplify 28/42 2 28 42 7 14 21 2 3 The fraction 28/42 simplifies to 2/3 (The GCF was used: 28/14 = 2, 42/14 = 3)

  30. Simplify 12/40 2 12 40 2 6 20 3 10 The fraction 12/40 simplifies to 3/10 (The GCF was used: 12/4 = 3, 40/4 = 10)

More Related