Puzzle Can you draw this without going over the same line twice and without taking your pen off the page?

Multiples, factors and primes

To revise the definitions of multiples factors and primes

To understand the meanings of HCF and LCM

To learn an algorithm to computes the HCF and LCM

Recap- multiplesWrite down the first five multiples of:

a) 3

b)5

c) 4

d)11

e)9

a)3, 6, 9, 12, 15

b)5, 10, 15, 20, 25, 30

c)4, 8, 12, 16, 20

d)11, 22, 33, 44, 55

e)9, 18, 27, 36, 45

Definition

• Product – An answer to a multiplication problem.

7 x 8 = 56Product

Definition• Factor – a number that divides into

another number WITHOUT a remainder

7 x 8 = 56

Factors – because 56 ÷ 8 = 7

What are the other factors of 56?

1, 2, 4, 7, 8, 14, 38, 56

Definition

• Prime Number – a number that has exactly two factors, itself and 1.

What are the first ten prime numbers?

2, 3, 5, 7, 11, 13, 17, 19, 23, 27

Prime factor decompositionWrite the number 36 as the product of its prime factors

36

2 18

2

2

9

3 3

2

3 336 = 2 x 2 x 3 x 336 = 22 x 32

Prime factor decompositionWrite the number 28 as the product of its prime factors

28

7 4

2

7

22

28 = 2 x 2 x 728 = 22 x 7

2

Prime factor decomposition

HCF and LCM

HCF is Highest Common Factor

LCM is Lowest Common Multiple

The HCF of 18 and 24 is…6

The LCM of 12 and 15 is… 60

1. Use a factor tree to help you find the Prime Factors

2.Then a Venn Diagram to help you find the HCF and LCM

Find the HCF and LCM of 24 and 60

FACTOR TREES

24 60

4 6 4 15

2 2 2 3 2 2 3 5

2460

Venn Diagram24 = 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

22

3

2 5

HCF = 2 x 2 x 3 = 12LCM = 2 x 2 x 2 x 3 x 5 = 120

HCF is the region of intersection2 x 2 x 3 = 12

LCM is all the numbers in the circles

multiplied together 2 x 2 x 2 x 3 x 5=120