1. {8, 16, 24, 32, …} are the multiples of 8 Common Multiples
{1, 2, 3, 4, …} = Counting Numbers
Multiplying the counting numbers by a particular number gives us multiples.
Eg {1, 2, 3, 4, …}
× 8
{8, 16, 24, 32, …} are the multiples of 8
Common Multiples
Multiples of 2 - {2, 4, 6, 8, 10, 12,…20, 22, …30..}
Multiples of 5 - {5, 10, 15, 20, 25, 30, 35,…}
LCM

2. Do these:
1) List the first 5 multiples of: a) 4 b) 12 c) 200
2) List all the multiples of 25 that are less than 140
3) True or false? a) 8 is a multiple of 2
b) 51 is a multiple of c) 37 is a multiple of 3
d) 25 is a multiple of 30.
4) Write down the first 3 numbers in each of these: a) Common multiples of 5 and 3
b) Common multiples of 10 and 15
5) LCM of 6 and ) LCM of 30 and 45
6-7 mins

3. Factors of a number are all the counting numbers that divide into it exactly.
Eg Factors of Use calculator
78÷1 = 78 → 78 and 1 are both factors
78÷2 = 39 → 2 and 39 are factors
78÷3 = 26 → 3 and 26 are factors
4,5 do not divide into 78 exactly.
78÷6 = 13 → 6 and 13 are factors
Therefore the factors of 78 are {1, 2, 3, 6, 13, 26, 39 and 78}

4. Write down the factors of : a) 7 b) 24 c) 80
Common factors
eg common factors of 18 and 60
Factors of 18 = {1, 2, 3, 6, 9, 18}
Factors of 60 = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60} HCF (highest common factor) is 6
Write down the common factors of : a) 15 and 20 b) 18, 24 and 30
What are the HCF’s of the numbers in 1).

5. What is the largest possible size for these square pieces?
A piece of material has the shape of a rectangle. It measures 96cm by 64cm. It is to be cut into square pieces. All of these are to be equal in size.
What is the largest possible size for these square pieces?
96cm
64cm
Factors of 96 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64}
Factors of 64 = {1, 64, 2, 32, 4, 16, 8}

6. Prime numbers Have only 2 factors, itself and 1. eg. 3, 5, 17, 29, 41
Numbers that have more than 2 factors are called composite numbers.
Any composite number can be written by multiplying only prime numbers. 28 = 2×2×7

7. So, 40=2×2×2×5
Factor tree

8. Draw factor trees for these:
a) b) c) 250
5 mins

9. You