numbers, like everything else, can be split up into smaller parts. for atoms, these smaller parts...

Numbers, like everything else, can be split up into smaller parts.

For atoms, these smaller parts are called quarks.

For numbers, they are called: _ _ _ _ _ _ _F A C T O R S

The Horseshoe Method

1 x 30 2 x 15

3 x 10

30

5 x 6

12356

101530

Divisibility

• How can we tell if a number divides by 2?

• How can we tell if a number divides by 5?

• Can you come up with any rules for the other numbers?

Divisibility Rules• 2: The last digit is even (0, 2, 4, 6, 8)• 3: Digits add up to a multiple of 3• 4: The last 2 digits make a multiple of 4• 5: The last digit is 0 or 5• 6: The number divides by 2 and 3• 7: (Nothing easy – sorry! Just try dividing)• 8: The last 3 digits make a multiple of 8• 9: Digits add up to a multiple of 9• 10: The last digit is 0

Some numbers cannot be broken down at all

• These are called: _ _ _ _ _ numbers

Eg: 17 = 1 x 17. (No other factors)

• Find the first 7 prime numbers.

(prime numbers have exactly 2 factors, so 1 is not a prime, but 2 is a prime)

P R I M E

2 3 5 7 11 13 17

12 18

3 4

2 2

36

2 3

Every number can be broken down until it is just prime

numbers multiplied together.

2 x 2 x 3 2 x 3 x 3

10 42

Does it divide by 10? By 5? By 2? By 3?

If none, check 7, 11, ...

Otherwise, prime.

22 215

7 3

420 = 22×3×5×7

Use the factor tree method to break down these numbers into their smallest parts (‘prime factors’)

28

32

45

100

68

5050

48

19

891

12 18

3 4

2 2

36

2 3

2 x 2 x 3 2 x 3 x 3

2 x 3 x 32 x 2 x 3

181212 183 2 2= x x 32 3 xx =HCF: 2 x 3 = 6

LCM: 2 x 2 x 3 x 3 = 36

50 70

5 10

2 5

710

2 5

2 x 5 x 5 2 x 5 x 7

50 702 x 5 x 72 x 5 x 5

50 705 2 5= x x 72 5 xx =HCF: 2 x 5 = 10

LCM: 2 x 5 x 5 x 7= 350