2. Factors, Primes & Composite Numbers by Ms. Green

3. Objectives  Students will be able to…  Compare and Contrast Prime and Composite Numbers  Use factor trees to find prime numbers  Use Divisibility Rules to find factors of numerbers

4. Definition  Product – An answer to a multiplication problem. 7 x 8 = 56 Product

5. Definition  Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

6. Definition  Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

7. What are the factors? 6 x 7 = 42 7 x 9 = 63 8 x 6 = 48 4 x 9 = 36 6 & 7 7 & 9 8 & 6 4 & 9

8. What are the factors? 42 ÷ 7 = 6 63 ÷ 9 = 7 48 ÷ 6 = 8 36 ÷ 9 = 4 7 9 6 9

9. Definition  Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

10. Examples of Prime Numbers 2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

11. Definition  Composite number – a that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

12. Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

13. Our Lonely 1 Special Note: One is not a prime nor a composite number. It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors.

14. Definition  Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 or 2 x 3 = 12 2

15. How to Do Prime Factorization Using a Factor Tree 48 Step 1 – Start with a composite number. Step 2 – Write down a multiplication problem that equals this number or any pair of factors of this number. 6 x 8 = 48

16. How to Do Prime Factorization Using a Factor Tree Step 3 – Find factors of these factors. 6 x 8 = 48 2 x 3 x 2 x 4 = 48

17. How to Do Prime Factorization Using a Factor Tree Step 4 – Find factors of these numbers until all factors are prime numbers. 6 x 8 = 48 2 x 3 x 2 x 4 = 48 2 x 3 x 2 x 2 x 2 = 48

18. How to Do Prime Factorization Using a Factor Tree Step 5 – Write the numbers from least to greatest. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48

19. How to Do Prime Factorization Using a Factor Tree Step 6 – Count how many numbers are the same and write exponents for them. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48 2 x 3 = 48 4

20. Prime factor this number 8 2 x 4 2 = 8 3 = 8 2 x 2 x 2 = 8

21. Prime factor this number 9 3 x 3= 9 3 = 9 2

22. Prime factor this number 16 4 x 4 2 = 16 4 = 16 2 x 2 x 2 x 2 = 16

23. Prime factor this number 18 3 x 6 2 x 3 = 18 2 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18

24. Prime factor this number 21 3 x 7= 21

25. Prime factor this number 22 2 x 11= 22

26. Divisibility Rules How do we know when we can divide one number into another exactly?

27. Divisibility Rules (2)  A number can be divided by 2 if  the last digit is even

28. Divisibility Rules (4)  a number is divisible by 4 if  the number made by the last two digits can be divided by 4

29. Divisibility Rules (5)  A number is divisible by 5 if  the last digit is a 5 or a 0

30. Divisibility Rules (6)  A number can be divided by 6 if  the last digit is even and the sum of all the digits is 3, 6 or 9

31. Divisibility Rules (8)  A number is divisible by 8 if  the number made by the last three digits will be divisible by 8

32. Divisibility Rules (9)  A number is divisible by 9 if  the sum of all the digits will add to 9

33. Divisibility Rules (10)  A number can be divided by 10 if  the last digit is a 0

34. Divisibility Rules  A number can be divided by 7 if  ……………… can you find a rule?

35. Divisibility Rules  2, the last digit will be an even number  3, all the digits will add to 3,6 or 9  4, the number made by the last two digits can be divided by 4  5, the last digit will be a 5 or 0

36. Divisibility Rules  6, the last digit will be even and the digits will add to 3, 6 or 9  8, the number made by the last three digits will be divisible by 8

37. Divisibility Rules  9, the sum of the digits will be 9  10, the last digit will be a 0  There is no easy test for 7, although some methods have been invented, however it is easier to use a pencil and paper method.

38. Practice  Go to these websites to practice using factor trees: Factors and Multiples Pythagoras’ Factor Game  Go to this website to practice using divisibility rules: Vector Kids Vector Kids  Homework time!  Complete the Prime Factorization and the divisibility rules handout!