Unit 1 Pupil Book 5-7 Math Worksheet Page 5
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10.3 Prime factor decomposition
.3 Prime factor decomposition
§ §
Find the lowest common multiple and the highest common factor
§
§
Find and use the prime factor decomposition of a number
§
§
Understand and use the index laws for multiplication and division
of numbers in index form
§
§
Use the index laws for numbers
§
§
The lowest common multiple (LCM) of two numbers is the
lowest number that is a multiple of them both.
Level 5
&
Level 6
§ §
The highest common factor (HCF) of two numbers is the highest number that is
a factor of them both.
Level 5
&
Level 6
§ §
You can write any number as the product of its prime factors.
2
For example 90
2
3
3
5 or 2
3
5.
Level 6
§ §
You can use the prime factor decomposition to fi nd the HCF and LCM of two
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numbers quickly.
Level 6
§
§
2
4
2
4
6
To multiply powers of the same number, add the indices.
3
3
3
3
The 20th-century
4
2
4
2
2
To divide powers of the same number, subtract the indices.
3
3
3
3
composer Messiaen
Level 6
&
Level 7
wrote a piece of
§ §
0
0
0
Any number to the power zero is 1. For example 3
1, 5
1, 35
1.
music that used
Level 7
prime numbers to
§ §
Negative powers can be written as unit fractions or decimals.
create unpredictable
__
___
____
1
1
1
For example 10
1
0.1, 10
2
0.01, 10
3
0.001.
Level 7
10
100
1000
rhythms.
Level 5
Find all the factor pairs for these numbers.
I can fi nd all the
factor pairs for
a
56
b
72
c
48
d
120
any whole number
I can fi nd the
Find the highest common factor (HCF) of these numbers.
HCF of two
a
30 and 42
b
27 and 45
c
18 and 66
d
96 and 144
numbers
I can fi nd the
Find the lowest common multiple (LCM) of these numbers.
LCM of two
7 and 9
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63 , …
numbers
Multiples of 9: 9, 18, 27, 36, 45, 54, 63 , …
LCM = 63
a
12 and 20
b
15 and 25
c
30 and 42
d
33 and 121
Level 6
Find the prime factor decomposition of these numbers.
180
180
Look for a pair of factors, neither of which is 1.
I can fi nd
the prime factor
Circle the factor if it is a prime number.
decomposition of a
18
10
Continue until no further factor pairs are possible.
whole number
2
2
180 = 2
2
3
3
5 or 2
3
5
×
×
×
×
×
×
3
6
2
5
a
30
b
42
c
72
d
99
2
3
factor
highest common factor (HCF)
index (indices)
index law
index form
8
Getting things in order
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