Transcript 2 - TheChalkface

Numbers, like everything else, can be split
up into smaller parts.
For atoms, these smaller parts are called
quarks.
FA
For numbers, they are called: _
_ C_ T_ O
_R
_S
_
The Horseshoe Method
30
1
2
x
x
3
x
x
5
1
2
30 3
15 5
6
10
10
6
15
30
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: P
_R
_ I_M_E_ 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)
2
3
5
7
11
13
17
12
18
Every number can be broken
down until it is just prime
numbers multiplied together.
3
6
4
2
2
2x2x3
2
3
3
2x3x3
Does it divide by 10?
By 5? By 2? By 3?
If none, check 7, 11, ...
Otherwise, prime.
420 = 22×3×5×7
10
42
2
5
21
2
7
3
Use the factor tree method to break
down these numbers into their
smallest parts (‘prime factors’)
28
100
48
32
68
19
45
5050
891
12
18
3
6
4
2
2
2x2x3
2
3
3
2x3x3
12 HCF:
3 222 2x33 =36 18
=
2x2x3
x
x x
x
=
2x3x3
LCM: 2 x 2 x 3 x 3 = 36
50
5
70
10
10
2
5
2x5x5
2
7
5
2x5x7
50 HCF:
5 222 x 555 = 10
7 70
=
2x5x5
x
x x
x
=
2x5x7
LCM: 2 x 5 x 5 x 7= 350