1. Greatest Common Factor Least Common Multiple Factorization

2. Why Factor? Factors allow you to break composite numbers down to their component parts. Factors allow you to break composite numbers down to their component parts. Factors are used to simplify fractions. Factors are used to simplify fractions. Factors are used to identify the greatest common factor (GCF) and the least common multiple (LCM). 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. 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 Start with 1: 1 x 24 = 24 2: 2 x 12 = 24 2: 2 x 12 = 24 3: 3 x 8 = 24 3: 3 x 8 = 24 4: 4 x 6 = 24 4: 4 x 6 = 24 6: 6 x 4 = 24 6: 6 x 4 = 24 8: 8 x 3 = 24 8: 8 x 3 = 24 12: 12 x 2 = 24 12: 12 x 2 = 24 24: 24 x 1 = 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. Prime numbers are numbers that have only one and the number as factors. “1” is neither prime or composite. “1” is neither prime or composite. Composite numbers can be written as products of their prime factors. Composite numbers can be written as products of their prime factors.

5. Upside Down Division Factorization

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

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

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

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

10. Greatest Common Factor (GCF) Definition: Definition: –The largest factor that divides evenly into 2 or more numbers. Examples: 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. Use Factorization Greatest Common Factor

12. Prime factor 28 and 16 to find the GCF 2 28 2 28 2 14 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 28 2 14 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 2 28 42 714 21 2 3 The GCF is the product of the common prime factors: 2 x 7 = 14 G

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

18. Use Factorization Least Common Multiple

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 42 714 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 5 10 30 2 2 6 1 3 GCF: 5 x 2 = 10 LCM: 5 x 2 x 1 x 3 = 30 G

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

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

27. Greatest Common Factor Simplifying Fractions

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)