1. Factors & Multiples

2. Essential Question: How can we determine if a number is prime or composite? Common Core Objective: 6.NS.2 Students will be able to describe the difference between a prime and composite number and use book ends to determine the list of factors for a given number with 80% accuracy. Factors & Multiples

3. Vocabulary:  Factor – a number that divides into a whole number with a remainder of zero.  Prime Number – a whole number that has exactly two unique factors, 1 and the number itself.  Composite Number – a number greater than 1 with more than two factors.  Prime Factorization – a composite number expressed as a product of prime numbers. Factors & Multiples

4. Before we get started lets do a little brain activity… Lets name all the different numbers we can multiply to get 28 1 x 28 2 x 14 4 x 7 Well guess what, these numbers have a special name…they’re called factors. Factors come in pairs…like for the number 28. Factors & Multiples

5. A PRIME number is… A number with only two factors, 1 and itself. Some Examples: 2, 3, 5, 7, 11, 13 A COMPOSITE number is… A number with more than 2 factors. Some Examples: 6, 8, 9, 10, 12, 14, 15 Factors & Multiples

6. Finding Factors of a Number Example 1: Find the factors of 12. Is it prime or composite? Factors & Multiples

7. Finding Factors of a Number Example 1: Find the factors of 12. Is it prime or composite? Factors & Multiples 1 x 12

8. Finding Factors of a Number Example 1: Find the factors of 12. Is it prime or composite? Factors & Multiples 1 x 12 2 x 6

9. Finding Factors of a Number Example 1: Find the factors of 12. Is it prime or composite? Factors & Multiples 1 x 12 3 x 4 2 x 6

10. Finding Factors of a Number Example 1: Find the factors of 12. Is it prime or composite? Factors & Multiples 1 x 12 3 x 4 2 x 6 12: 1, 2, 3, 4, 6, 12 Composite

11. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples

12. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples 1 x 24

13. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples 2 x 12 1 x 24

14. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples 2 x 12 3 x 8 1 x 24

15. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples 2 x 12 4 x 6 3 x 8 1 x 24

16. Finding Factors of a Number Example 2: Find the factors of 24. Is it prime or composite? Factors & Multiples 2 x 12 4 x 6 3 x 8 24: 1, 2, 3, 4, 6, 8, 12, 24 1 x 24 Composite

17. Finding Factors of a Number Example 3: Find the factors of 17. Is it prime or composite? Factors & Multiples

18. Finding Factors of a Number Example 3: Find the factors of 17. Is it prime or composite? Factors & Multiples 1 x 17

19. Finding Factors of a Number Example 3: Find the factors of 17 and then identify as prime or composite. Factors & Multiples 1 x 17 17: 1, 17 Prime

20. Finding Factors of a Number Example 4: Find the factors of 2. Is it prime or composite? Factors & Multiples

21. Finding Factors of a Number Example 4: Find the factors of 2. Is it prime or composite? Two is a VERY special number for a reason we are about to see… Factors & Multiples

22. Finding Factors of a Number Example 4: Find the factors of 2. Is it prime or composite? Two is a VERY special number for a reason we are about to see… Factors & Multiples 1 x 2 2: 1, 2

23. Finding Factors of a Number Example 4: Find the factors of 2. Is it prime or composite? Two is a VERY special number for a reason we are about to see… Two is the ONLY EVEN PRIME NUMBER !!!!!!!!!!!!!!!!!!!! wow that is awesome! Factors & Multiples 1 x 2 2: 1, 2

24. Finding multiples is just like multiplying the number by 1, then 2, then 3, then 4, and so on… This is why it called finding the MULTIPLES (you are MULTIPLying) Factors & Multiples

25. Finding Multiples of a Number Example 5: Find the first five multiples of 8. Factors & Multiples

26. Finding Multiples of a Number Example 5: Find the first five multiples of 8. 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 Factors & Multiples

27. Finding Multiples of a Number Example 5: Find the first five multiples of 8. 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 Factors & Multiples Therefore…to express the first five multiples of 8, your answer would look like:

28. Finding Multiples of a Number Example 5: Find the first five multiples of 8. 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 Factors & Multiples 8: 8, 16, 24, 32, 40, … Therefore…to express the first five multiples of 8, your answer would look like:

29. Finding Multiples of a Number Example 6: Find the first 8 multiples of 15. Factors & Multiples

30. Finding Multiples of a Number Example 6: Find the first 8 multiples of 15. 15 x 1 = 15 15 x 2 = 30 15 x 3 = 45 15 x 4 = 60 15 x 5 = 75 15 x 6 = 90 15 x 7 = 105 15 x 8 = 120 Factors & Multiples

31. Finding Multiples of a Number Example 6: Find the first 8 multiples of 15. 15 x 1 = 15 15 x 2 = 30 15 x 3 = 45 15 x 4 = 60 15 x 5 = 75 15 x 6 = 90 15 x 7 = 105 15 x 8 = 120 Factors & Multiples Therefore…to express the first 8 multiples of 15, your answer would look like:

32. Finding Multiples of a Number Example 6: Find the first 8 multiples of 15. 15 x 1 = 15 15 x 2 = 30 15 x 3 = 45 15 x 4 = 60 15 x 5 = 75 15 x 6 = 90 15 x 7 = 105 15 x 8 = 120 Factors & Multiples 15: 15, 30, 45, 60, 75, 90, 105, 120 … Therefore…to express the first 8 multiples of 15, your answer would look like:

33. Guided Practice Problems Directions: Find all the factors of each number and identify as prime or composite. 1. 25 2. 100 3. 49 4. 23 Factors & Multiples

34. Guided Practice Problems Directions: Find all the factors of each number and identify as prime or composite. 1. 25 => 25: 1, 5, 25 (composite) 2. 100 => 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 (composite) 3. 49 => 49: 1, 7, 49 (composite) 4. 23 => 23: 1, 23 (prime) Factors & Multiples

35. Independent Practice Problems Directions: Find all the factors of each number and identify as prime or composite. 1. 36 2. 37 3. 42 4. 80 Factors & Multiples

36. Independent Practice Problems Directions: Find all the factors of each number and identify as prime or composite. 1. 36 => 36: 1, 2, 3, 4, 6, 9, 12, 36 (composite) 2. 37 => 37: 1, 37 (prime) 3. 42 => 42: 1, 2, 3, 6, 7, 14, 21, 42 (composite) 4. 80 => 23: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 (composite) Factors & Multiples

37. Guided & Independent Practice Problems Directions: Find the first 4 multiples of each number. 1. 5 2. 9 3. 16 4. 120 Factors & Multiples

38. Guided & Independent Practice Problems Directions: Find the first 4 multiples of each number. 1. 5 => 5: 5, 10, 15, 20,… 2. 9 => 9: 9, 18, 27, 36,… 3. 16 => 16: 16, 32, 48, 64,… 4. 120 => 120: 120, 240, 360, 480,… Factors & Multiples

39. Homework p.158 #1-4, 9-12, all Factors & Multiples