Download Prime Factors/Indicies

Prime Factors/ Indices
Objectives
By the end of the lesson learners will be able to:
• Identify Prime Factors (Process of the Factor Tree)
• Express a number as a product of its prime factors.
• Identify the LCM and LCF using Venn diagrams.
• Use powers (also known as indices)
Prime Factors
• We can use a ‘factor tree’ to enable us to write a number as “a
product of its prime factors”
• Each time you reach a prime number, you stop and circle that number
• Example: Write 84 as a product of its prime factors
84
2
42
2
• 84 = 2 x 2 x 3 x 7
• 84 = 22 x 3 x 7
21
3
7
Prime Factors
• Write 420 as a product of prime factors.
Your turn…
1. Find the HCF of the
following:
2. Find the LCM of the
following:
a)
b)
c)
d)
e)
f)
a)
b)
c)
d)
e)
f)
18 and 28
16 and 40
42 and 90
40 and 63
20, 64 and 108
54, 90 and 162
2
8
6
1
4
18
4 and 5
8 and 12
6 and 9
12 and 15
5, 8 and 10
4, 7 and 9
20
24
18
60
40
252
3. Write the following as products of their prime factors.
2 x 7 x 11
32 x 2
33 x 5
2 x 3 x 5 x 7 x 11
a) 18
b) 135
c) 154
d) 2310
HCF and LCM
• Calculate the HCF and LCM of 48 and 60
48
48 = 2 x 2 x 2 x 2 x 3
60
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
HCF = 2 x 2 x 3 = 12
LCM = 2 x 2 x 3 x 2 x 2 x 5 = 240
Find the HCF and
LCM of the
following:
24 and 30
36 and 50
48
60
16 and 72
• Multiply the numbers in the overlap to get the HCF
• Multiply all the numbers in the Venn diagram to get the
LCM.
3
5
5
8
Introduction
2
What does 4 actually mean?
4×4
16
Introduction
5
What does 4 actually mean?
4×4×4×4×4
Introduction
How can we write 5×5×5×5
5
4
This is 5×5×5×5 written in INDEX FORM
Writing in Index Form
Write the following in Index Form
• 8×8×8×8
= 84
6
• 3×3×3×3×3×3 =
3
• 9×9×9
= 93
Indices
• 3x3x3x3
=3
4
• 3x3x3
=3
3
• 3x3
=3
2
• 3
=3
1
Multiplying Indices
Simplify the following leaving in index
form.
3
4
3
4
•
88 × 8 8 =
8×8×8
× 8×8×8×8
=8
7
Is there a quick way you can work this out?
•
3
4
8 ×8
3
=
4
8
+
=8
7
Remember this only works for numbers with the
Same base number
Multiplying Indices
Simplify the following leaving in index
form.
2
4
2
4
•
55 × 5 5 =
5×5
× 5×5×5×5
=5
6
The Quick Way!!!
•
2
4
5 ×5
2
=
4
5
+
=5
6
Remember this only works for numbers with the
Same base number
Dividing Indices
Simplify the following leaving in index
form.
5
2
5
2 x 2 x 2 x 2 x
25
1. 22 ÷ 2 2=2
=
2 x 2
22
=2
3
The Quick Way!!!
1.
5
2
2 ÷2
5
=
2
2
-
=2
3
Remember this only works for numbers with the
Same base number
2
Indices
Simplify the following leaving in index
form.
3
3
3
1. (( 2 ) 2
2 x2
This means this
=2
6
For these it is best to write them out!
Remember this only works for numbers with the
Same base number
Indices
Simplify the following leaving in index
form.
5
5
5
5
1. (( 3 ) 3
3 x3 x3
This means this
=3
For these it is best to write them out!
Remember this only works for numbers with the
Same base number
15
Questions
Simplify the following numbers, leaving your answers in index form:
1. (a)
23 x 22
25
(b)
35 x 32
37
(c)
73 x 7
74
(d)
95 x 92
97
2. (a)
23 ÷ 22
(b)
35 ÷ 32
(c)
73 ÷ 7
(d)
95 ÷ 92
2
33
72
93
Indices with Letters
• axaxaxa
• axaxa
• axa
=a
4
=a
3
=a
2
=a
1
• a
Multiplying Indices
Simplify the following leaving in index
form.
3
4
3
4
•
aa × a a =
× a×a×a×a
a×a×a
=a
7
Is there a quick way you can work this out?
•
3
4
a ×a
3
=
4
a
+
=a
7
Remember this only works for numbers with the
Same base number
Indices with Letters
a55 x 2a2
33a
=
3xaxaxaxaxa
=
3 x 2x
=
6a7
a
x
2xaxa
x a x a x a x a x a x a
Indices with Letters
66aa33 x 33aa22
=
6 x a x a
x
a
x
=
6 x 3 x a x a x a
=
18a5
3 x a x a
x
The Quick Way!!!
66aa33 x 33aa222
=
x
x
a
+
= 18a5
axa
Questions
Simplify the following numbers, leaving your answers in index form:
1. (a)
a3 x a2
(b)
a5
2. (a)
a5 x a6
(c)
a x a3
a11
(23)2
26
3
(b)
5
3. (a) 3b x 7b
8
21b
a2 x a12
a4
(35)2
310
(c)
7
(b) 5b x 2b
10b8
(d)
a
(73)3
79
3
(d)
3
(c) 2b x 6b
12b6
14
(92)5
10
9
3
2
(d) 2b x 15b
5
30b