1. Whole Number Arithmetic Factors and Primes

2. Exercise 5 - Oral examples { factors of 15 } { factors of 32 } { factors of 27 } { factors of 28 } (1, 3, 5, 15) (1, 2, 4, 8, 16, 32) (1, 3, 9, 27) (1, 2, 4, 7, 14, 28)

3. Exercise 5 - Written examples 1){ factors of 4 } 2){ factors of 9 } 3){ factors of 16 } 4){ factors of 25 } 5){ factors of 36 } 6){ factors of 1 } 7){ factors of 6 } 8){ factors of 12} (1, 2, 4) (1, 3, 9) (1, 2, 4, 8, 16) (1, 5, 25) (1, 2, 3, 4, 6, 9, 12, 18, 36) (1) (1, 2, 3, 6) (1, 2, 3, 4, 6, 12)

4. Exercise 5 - Written examples 9){ factors of 18 } 10){ factors of 24 } 11){ factors of 10 } 12){ factors of 20 } 13){ factors of 30 } 14){ factors of 40 } 15){ factors of 2 } 16){ factors of 3} (1, 2, 3, 6, 9, 18) (1, 2, 3, 4, 6, 8, 12, 24) (1, 2, 5, 10) (1, 2, 4, 5, 10, 20) (1, 2, 3, 5, 6, 10, 15, 30) (1, 2, 4, 5, 8, 10, 20, 40) (1, 2,) (1, 3)

5. Exercise 5 - Written examples 17){ factors of 5 } 18){ factors of 7} 19){ factors of 11 } 20){ factors of 13 } (1, 5) (1, 7) (1, 11) (1, 13)

6. Prime Numbers 1)Prime numbers have exactly 2 factors ( namely 1 and itself). 2)If a factor is a prime number then it is called a prime factor. { factors of 100 } = {1, 2, 4, 5, 10, 20, 25, 50, 100 } { prime factors of 100 } = { 2, 5 }

7. Prime Numbers The number 1 is not a prime number and so it is not a prime factor of any number.

8. Exercise 5 - Written examples 21){ prime numbers between 0 and 10 } 22){ prime numbers between 10 and 20 } 23){ prime numbers between 20 and 30 } 24){ prime numbers between 30 and 40 } (2, 3, 5, 7) (11, 13, 17, 19) (23, 29) (31, 37)

9. 25) { prime factors of 6 } Factors of ‘ 6 ’ are 1, 2, 3, 6 Prime factors of ‘ 6 ’ are 2, 3

10. 26) { prime factors of 10 } Factors of ‘ 10 ’ are 1, 2, 5, 10 Prime factors of ‘ 10 ’ are 2, 5

11. 27) { prime factors of 14 } Factors of ‘ 14 ’ are 1, 2, 7, 14 Prime factors of ‘ 14 ’ are 2, 7

12. 28) { prime factors of 15 } Factors of ‘ 15 ’ are 1, 3, 5, 15 Prime factors of ‘ 15 ’ are 3, 5

13. 29) { prime factors of 21 } Factors of ‘ 21 ’ are 1, 3, 7, 21 Prime factors of ‘ 21 ’ are 3, 7

14. 30) { prime factors of 35 } Factors of ‘ 35 ’ are 1, 5, 7, 35 Prime factors of ‘ 35 ’ are 5, 7

15. 31) { prime factors of 30 } Factors of ‘ 30 ’ are 1, 3, 5, 6, 10, 30 Prime factors of ‘ 30 ’ are 3, 5

16. 32) { prime factors of 42 } Factors of ‘ 42 ’ are 1, 2, 3, 6, 7, 14, 21, 42 Prime factors of ‘ 42 ’ are 2, 3, 7

17. Multiples 33){ multiples of 3 } 34){ multiples of 6 } 35){ multiples of 2 } 36){ multiples of 4 } 3, 6, 9, 12, … 6, 12, 18, 24,,… 2, 4, 6, 8, … 4, 8, 12, 16, …

18. 41){ factors of 60 } 42){ factors of 360 } 43){ prime numbers between 40 and 50 } 44){ prime numbers between 50 and 60 } (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360) (41, 43, 47) (53, 59)

19. Exercise 6 - Prime factors 42 67

20. Prime factors 42 67 ‘7’ is a prime number

21. Prime factors 42 67 23 2, 3, and 7 are all prime numbers

22. Product of prime factors 42 67 23

23. Exercise 6 - Prime factors 28 47

24. Prime factors 28 47 ‘7’ is a prime number

25. Prime factors 28 47 22 2, and 7 are all prime numbers

26. Product of prime factors 28 47 22

27. Exercise 6 - Prime factors 64 88

28. Prime factors 64 88 2 4 2 4

29. Prime factors 64 88 2 4 2 4 2 22 2

30. Product of Prime factors 64 88 2 4 2 4 2 22 2

31. Exercise 6 - Prime factors 72 89

32. Prime factors 72 89 2 4 3 3

33. Prime factors 72 89 2 4 3 3 2 2

34. Product of Prime factors 72 89 2 4 3 3 2 2

35. Exercise 6 Write these numbers as products of their primes 1) 6 2) 10 3) 14 4) 15 5) 21 6) 35 7) 30 8) 70 2 x 3 2 x 5 2 x 7 3 x 5 3 x 7 5 x 7 2 x 3 x 5 2 x 5 x 7

36. Exercise 6 9) 4 10) 8 11) 16 12) 32 13) 9 14) 27 15) 25 16) 49 2 x 2 = 2 2 2 x 2 x 2 = 2 3 2 x 2 x 2 x 2 = 2 4 2 5 3 x 3 = 3 2 3 x 3 x 3 = 3 3 5 x 5 = 5 2 7 x 7 = 7 2

37. Exercise 6 17) 12 18) 18 19) 20 20) 50 21) 45 22) 75 23) 36 24) 60 2 x 2 x 3 = 2 2 x 3 2 x 3 x 3 = 2 x 3 2 2 x 2 x 5 = 2 2 x 5 2 x 5 x 5 =2 x 5 2 5 x 3 x 3 = 5 x 3 2 3 x 5 x 5 = 3 x 5 2 2 x 2 x 3 x 3 = 2 2 x 3 2 2 x 2 x 3 x 5 = 2 2 x 3 x 5

38. Exercise 6 25) 24 26) 54 27) 40 28) 56 29) 48 30) 80 31) 90 32) 84 2 3 x 3 2 x 3 3 2 3 x 5 7 x 2 3 2 4 x 3 2 4 x 5 2 x 3 2 x 5 2 2 x 3 x 7

39. Exercise 6 33) Find the smallest number which is the product of 4 different prime factors. 2 x 3 x 5 x 7 = 210

40. Exercise 6 - 34 Find the next smallest number which is the product of 4 different prime factors. 2 x 3 x 5 x 11 = 330

41. Exercise 6 - 35 Find the smallest number which is the product of 4 prime factors (not necessarily different). 2 x 2 x 2 x 2 = 16

42. Exercise 6 - 36 Find the next smallest number which is the product of 4 prime factors (not necessarily different). 2 x 2 x 2 x 3 = 24