Whole Number Arithmetic

1. Whole Number Arithmetic Factors and Primes

2. { 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) Exercise 5 - Oral examples

3. { factors of 4 } { factors of 9 } { factors of 16 } { factors of 25 } { factors of 36 } { factors of 1 } { factors of 6 } { 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) Exercise 5 - Written examples

4. { factors of 18 } { factors of 24 } { factors of 10 } { factors of 20 } { factors of 30 } { factors of 40 } { factors of 2 } { 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) Exercise 5 - Written examples

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

6. Prime Numbers 1)Prime numbers have exactly 2 factors ( namely 1 and itself). • 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. { prime numbers between 0 and 10 } { prime numbers between 10 and 20 } { prime numbers between 20 and 30 } { prime numbers between 30 and 40 } (2, 3, 5, 7) (11, 13, 17, 19) (23, 29) (31, 37) Exercise 5 - Written examples

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 of 3 } { multiples of 6 } { multiples of 2 } { multiples of 4 } 3, 6, 9, 12, … 6, 12, 18, 24,,… 2, 4, 6, 8, … 4, 8, 12, 16, … Multiples

18. { factors of 60 } { factors of 360 } { prime numbers between 40 and 50 } { 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 6 7

20. Prime factors 42 6 7 ‘7’ is a prime number

21. Prime factors 42 6 7 2 3 2, 3, and 7 are all prime numbers

22. Product of prime factors 42 6 7 2 3

23. Exercise 6 - Prime factors 28 4 7

24. Prime factors 28 4 7 ‘7’ is a prime number

25. Prime factors 28 4 7 2 2 2, and 7 are all prime numbers

26. Product of prime factors 28 4 7 2 2

27. Exercise 6 - Prime factors 64 8 8

28. Prime factors 64 8 8 4 2 2 4

29. Prime factors 64 8 8 4 2 2 4 2 2 2 2

30. Product of Prime factors 64 8 8 4 2 2 4 2 2 2 2

31. Exercise 6 - Prime factors 72 8 9

32. Prime factors 72 8 9 3 2 3 4

33. Prime factors 72 8 9 3 2 3 4 2 2

34. Product of Prime factors 72 8 9 3 2 3 4 2 2

35. 6 10 14 15 21 35 30 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 Exercise 6Write these numbers as products of their primes

36. 4 8 16 32 9 27 25 49 2 x 2 = 22 2 x 2 x 2 = 23 2 x 2 x 2 x 2 = 24 25 3 x 3 = 32 3 x 3 x 3 = 33 5 x 5 = 52 7 x 7 = 72 Exercise 6

37. 12 18 20 50 45 75 36 60 2 x 2 x 3 = 22 x 3 2 x 3 x 3 = 2 x 32 2 x 2 x 5 = 22 x 5 2 x 5 x 5 =2 x 52 5 x 3 x 3 = 5 x 32 3 x 5 x 5 = 3 x 52 2 x 2 x 3 x 3 = 22 x 32 2 x 2 x 3 x 5 = 22 x 3 x 5 Exercise 6

38. 24 54 40 56 48 80 90 84 23 x 3 2 x 33 23 x 5 7 x 23 24 x 3 24 x 5 2 x 32 x 5 22 x 3 x 7 Exercise 6

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

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

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

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