MultiplesMultiples

{1, 2, 3, 4, …} = Counting Numbers{1, 2, 3, 4, …} = Counting Numbers

Multiplying the counting numbers by a particular Multiplying the counting numbers by a particular number gives us multiples.number gives us multiples.

Eg. {1, 2, 3, 4, …}Eg. {1, 2, 3, 4, …}

× 8× 8

{8, 16, 24, 32, …} are the multiples of 8{8, 16, 24, 32, …} are the multiples of 8

Common MultiplesCommon Multiples

Multiples of 2 - {2, 4, 6, 8, Multiples of 2 - {2, 4, 6, 8, 1010, 12,…, 12,…2020, 22, …, 22, …3030..}..}

Multiples of 5 - {5, Multiples of 5 - {5, 1010, 15, , 15, 2020, 25, , 25, 3030, 35,…}, 35,…}LCM

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 17 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 9 6) LCM of 30 and 456-7 mins

FactorsFactors of a number are all the counting of a number are all the counting numbers that divide into it exactly.numbers that divide into it exactly.

Eg Factors of 78 Use calculatorEg Factors of 78 Use calculator

7878÷1 = 78 → 78 and 1 are both factors÷1 = 78 → 78 and 1 are both factors

78÷2 = 39 → 2 and 39 are factors78÷2 = 39 → 2 and 39 are factors

78÷3 = 26 → 3 and 26 are factors78÷3 = 26 → 3 and 26 are factors

4,5 do not divide into 78 exactly.4,5 do not divide into 78 exactly.

78÷6 = 13 → 6 and 13 are factors78÷6 = 13 → 6 and 13 are factors

Therefore the factors of 78 are {1, 2, 3, 6, 13, 26, Therefore the factors of 78 are {1, 2, 3, 6, 13, 26, 39 and 78}39 and 78}

Write down the factors of : a) 7 b) 24 c) 80Write down the factors of : a) 7 b) 24 c) 80

Common factorsCommon factors

eg common factors of 18 and 60eg common factors of 18 and 60

Factors of 18 = {Factors of 18 = {1, 2, 3, 61, 2, 3, 6, 9, 18}, 9, 18}

Factors of 60 = {Factors of 60 = {1, 2, 3,1, 2, 3, 4, 5, 4, 5, 66, 10, 12, 15, 20, 30, , 10, 12, 15, 20, 30, 60} HCF (highest common factor) is 60} HCF (highest common factor) is 66

1)1)Write down the common factors of : a) 15 and Write down the common factors of : a) 15 and 20 b) 18, 24 and 30 20 b) 18, 24 and 30

2)2)What are the HCF’s of the numbers in 1).What are the HCF’s of the numbers in 1).

A piece of material has the shape of a rectangle. A piece of material has the shape of a rectangle. It measures 96cm by 64cm. It is to be cut into It measures 96cm by 64cm. It is to be cut into square square pieces. All of these are to be pieces. All of these are to be equal equal in in size. size.

What is the largest possible size for these What is the largest possible size for these square pieces?square pieces?

Factors of 96 = {1, 2, 3, 4, 6, 8, 12, 16, 24, Factors of 96 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 3232, 48, , 48, 64} 64}

Factors of 64 = {1, 64, 2, Factors of 64 = {1, 64, 2, 3232, 4, 16, 8}, 4, 16, 8}

96cm96cm

64cm64cm

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

40

2 20

2 2 10

2 2 2 5

So, 40=2×2×2×5

Draw factor trees for these:Draw factor trees for these:

a) 48 b) 91 c) 250a) 48 b) 91 c) 250

5 mins

You