1. FACTORS and MULTIPLES
TOPIC: 1

2. FACTORS

3. Example 1
List all the factors of 12 12
1  12
2  6
3  4

4. 1 X 12 1 12 12
2 X 6 2 6
3 X 4 3 4
are ALL FACTORS of 12

5. A factor divides the numbers without leaving any remainder
So what is factor?

6. 2 6 12 12 NO REMAINDER To illustrate: Hence, 6 is a FACTOR of 12
(and 2 is another)

7. TEST YOURSELF!

8. Example 2
List all the factors of 20 20
1  20 20
2  10
4  5

9. The Factors of 20…. 2  10 4  5 Factors of 12 are: 1, 2, 4, 5, 10, 20
20 = 1  20
2  10
4  5
Factors of 12 are: 1, 2, 4, 5, 10, 20

10. MULTIPLES

11. Eg 1:List down the first three multiples of 4
Answer: 12 4 8

12. Eg 2: List down the first six multiples of 5
Answer: 5 10 15 20 25 30

13. Multiples are product of that number and any other number
So what are MULTIPLES?

14. TEST YOURSELF! Textbook page 5 Question 1 - 5
Try yourself Question 1 - 2
TEST YOURSELF!

15. Open the Box - Factors of numbers32
1, 32, 2, 16, 4, 8
1, 40, 2, 20, 4, 10, 5, 8
1, 18, 2, 9, 3, 6,
1, 100, 2,50, 4, 25, 5, 20, 10
1,28,2,14,4,7
1,55,5,11
1,29
1,35,5,7
1,68,2,34,4,17
1,37 40 18
100 28 55 29 35 68 37
What are all the factors of the numbers on the cards?

16. List down all the multiples of 3 between 13 and 25
Answer: 15 18 21 24

17. PRIMES
and
PRIME FACTORISATION

18. PRIME NUMBERS

19. List the factors of each of the number2 3 5 7 11 13 17 19 23 29
1 x 2
1 x 7
1 x 17
1 x 29
2,3,5,7,11,13,17,19,23,29
are called PRIME NUMBERS
1 x 3
1 x 11
1 x 19
1 x 5
1 x 13
1 x 23
Each number only have 2 factors! no other factors except for 1 and themselves!

20. A prime number is a number that has exactly two factors, 1 AND ITSELF!
What is a Prime Number?
A prime number is a number that has exactly two factors, 1 AND ITSELF!

21. P R I M E A C T O R S F

22. Eg1: List all the prime factor of …18 ?

23. The Factors of 18…. 2  9 3  6 Factors of 18: 1, 2, 3, 6, 9, 18
18 = 1  18
2  9
3  6
Factors of 18: 1, 2, 3, 6, 9, 18
Prime Factors of 18: 2, 3

24. Eg2: List all the prime factor of …30 ?

25. The Factors of 30….
30 = 1  30
2  15
3  10
5  6
Factors of 18: 1,2,3,5,6,10,15,18
Prime Factors of 30: 2,3,5,

26. P R I M E A C T O R I F A O N S I T

27. "Prime Factorization" is finding which prime numbers multiply together to make the original number.

28. Eg 1:Find the prime factor/prime factorization of …18 ?

29. Method 1: Factor Tree

30. The PRIME FACTORISATION of 18: 2 X 3 X 3 or 2 X 3² (index notation)9 3 3
The PRIME FACTORISATION of 18:
2 X 3 X 3 or 2 X 3² (index notation)

31. 18 9 3 1 Method 2: Continuous Division Find the Prime Factors of 18 2
2 X 3 X 3 or
2 X 3² 9 3 3 3 1
Note:
Start with the smallest prime number first!

32. Eg 2: Find the Prime Factors of..12

33. Method 1:Factor Tree Prime factors of 12: 2 X 2 X 3 or 2² X 3 12 3 4
Prime factors of 12: 2 X 2 X 3 or
2² X 3

34. 12 6 3 1 Method 2: Continuous Division 2 2 3 Prime factors of 12:
2 X 2 X 3 or
2² X 3 6 2 3 3 1
Note:
Start with the smallest prime number first!

35. TEST YOURSELF!

36. 60 30 15 5 1 2 2 3 5 Eg 3: Find the Prime Factors of 60
Method 2: Continuous Division 60 2
Prime factors of 60:
2 X 2 X 3 X 5 or
2² X 3 X 5 30 2 3 15 5 5
Note:
Start with the smallest prime number first! 1

37. Textbook page 7 Question 1 – 3
5 &6
TEST YOURSELF!

38. LOWEST COMMON MULTIPLE (LCM)

39. Eg 1:
Find the lowest common multiple of 2 and 6
Multiples of 2
2, 4, 6, 8, 10, 12, 14
Multiples of 6
6, 12, 18, 24, 30, 36
Answer:

40. ANOTHER METHOD: CONTINUOUS DIVISION

41. We stop dividing until you get all 1
Eg 1:Find the lowest common multiple (LCM) of 2 and 6 2 6 2 1 3 3 1 1
Note:
We stop dividing until you get all 1
The LCM of 2 and 6:
2 X 3 = 6

42. Eg 2: Find the lowest common multiple of 12 and 18 Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 12
Multiples of 18
18, 36, 54, 72, 90, 108, 126,……
Answer:

43. ANOTHER METHOD: CONTINUOUS DIVISION

44. We stop dividing until you get all 1
Eg 2:Find the lowest common multiple (LCM) of 12 and 18 12 18 2 6 9 2 9 3 3
The LCM of 12 and 18:
2 X 2 X 3 X 3 = 36 3 1 3
Note:
We stop dividing until you get all 1 1 1

45. LCM of two numbers is the smallest common multiple of these numbers
So what is Lowest Common Multiples(LCM)?

46. Textbook page 11 Question 2 &4
TEST YOURSELF!

47. Open the Box - Common Multiples
105 32 60 42
110 84
1512 98 63
660
15 and 21
8 and 32
30 and 20
6 and 42
22 and 55
42 and 28
27 and 56
14 and 49
63 and 9
60 and 220
What is the lowest common multiple for each pair of numbers? Lift the cover to answer the question

48. HIGHEST COMMON FACTOR (HCF)

49. Eg1: Find the Highest Common Factor of 10 and 15
10 = 1 x 10 2 x 5
15 = 1 x 15 3 x 5
Factors of 10:
Factors of 15: 1 2 5 10 1 3 5 15
Let’s look at an example. The factors of 10 are 1, 2, 5 and 10. The factors of 15 are 1, 3, 5 and 15. In other words, 10 and 15 share the common factor of 1 and 5. These are the common factors of 10 and 15.
Among these common factors of 10 and 15, the largest is 5. That’s the greatest common factor, also known as highest common factor. Easy, right?
Common factors of 10 and 15 : 1 and 5
Highest common factor : 5

50. ANOTHER METHOD: CONTINUOUS DIVISION

51. We stop dividing until both number have no common factor
Eg 1: Find the highest common factor (HCF) of 10 and 15 10 15 5 2 3
Note:
We stop dividing until both number have no common factor
The HCF of 10 and 15: 5

52. Eg 2: Find the highest Common Factor of 16 and 24
16 = 1 x 16 2 x 8 4 x 4
24 = 1 x 24
2 x 12
3 x 8
4 x 6
Factors of 16 1 2 4 8 16
Factors of 24 1 2 3 4 6 8 24
Common factors of 16 and 24 : 1,2,4,8
So what’s the highest common factor of 9 and 12?
That’s right, the common factors of 9 and 12 are 1 and 3 so 3 is the highest common factor.
Finding a highest common factor is easy in principle. First, find the factors of each number. Then, find the factors they share. Finally, take the highest of those common factors. That’s the highest common factor.
Highest Common Factor : 8

53. ANOTHER METHOD: CONTINUOUS DIVISION

54. We stop dividing until both number have no common factor
Eg 2: Find the highest common factor (HCF) of 16 and 24 16 24 2 8 12 2 4 6 2 2 3
Note:
We stop dividing until both number have no common factor
The HCF of 16 and 24:
2 x 2 x 2 = 8

55. Textbook page 11 Question 1 &3
TEST YOURSELF!

56. Open the Box - Common Factors
15 and 21 3 8 10 6 11 14 1 7 9 20
8 and 32
30 and 20
6 and 42
22 and 55
42 and 28
27 and 56
14 and 49
63 and 9
60 and 220
What is the highest common factor for these two numbers? Lift the cover to answer the question

57. Square, square root & Cube, cube root

58. Square & Square root How to Square A Number
To square a number, just multiply it by itself ...
Example: What is 3 squared?
3 Squared = 3 × 3 = 9
"Squared" is often written as a little 2 like this:
This says "4 Squared equals 16" (the little 2 says the number appears twice in multiplying)

59. = 3 Square & Square root A square root goes the other way:
"Square root" is often written as like this:
Example 1: What is √25?
√25 = 5
= 3
you would say "square root of 9 equals 3"

60. Square & Square root 2 484 √2 x 2 x 11 x 11 √(2 x 11) x (2 x 11
Example 2: Find the square root of 484 using prime factorisation 2
484
√2 x 2 x 11 x 11
√(2 x 11) x (2 x 11
√(2 x 11)²
Ans: 2 x 11
: 22 2
242 11
121 11 11 1

61. (the little "3" means the number appears three times in multiplying)
Cube & Cube root
How to Cube A Number
To cube a number, just use it in a multiplication 3 times
Example: What is 3 cubed?
3 cubed = 3 × 3 × 3 = 27
“cubed" is often written as a little 3 like this:
we write down "3 Cubed" as 33
(the little "3" means the number appears three times in multiplying)

62. Cube & Cube root 3 27 A cube root goes the other way:
“cube root" is often written as like this: 3 27
you would say "the cube root of 27 equals 3") 

63. Cube & Cube root 2 1728 2 864 ³√(2 x 2 x 3) ³ Ans: 2 x 2 x 3 : 12 2
Example 1: Find the cube root of 1728 using prime factorisation 2
1728 2
864
³√2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
³√(2 x 2 x 3) x (2 x 2 x 3) x (2 x 2 x 3)
³√(2 x 2 x 3) ³
Ans: 2 x 2 x 3
: 12 2
432 2
216
108 2 2 54 3 27 3 9 3 3 1

64. Order of Operations
 BODMAS
Free Powerpoint Templates

65. Operations
"Operations" mean things like add, subtract, multiply, divide, squaring, etc.
When you see something like...
7 + (6 × 52 + 3)
... what part should you calculate first?  Start at the left and go to the right?  Or go from right to left?
Calculate them in the wrong order, and you will get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:

66. Orders (ie Powers and Square Roots, etc.)
Order of Operations B
Brackets first O
Orders (ie Powers and Square Roots, etc.) DM
Division and Multiplication
(left-to-right) AS
Addition and Subtraction

67. Example 1 Example 2 How do you work out 3 + 6 × 2 ?
Multiplication before Addition:
First 6 × 2 = 12, then  = 15
Example 2
How do you work out (3 + 6) × 2 ?
Brackets first:
First (3 + 6) = 9, then 9 × 2 = 18
Oh, yes, and what about 7 + (6 × 52 + 3) ?