splitting the number
DESCRIPTION
Splitting the number. 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. 30. 1 2 3 5 6 10 15 30. 1 x 30. 2 x 15. - PowerPoint PPT PresentationTRANSCRIPT
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