multiples if a number divides exactly into another number, the second is a multiple of the first....
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![Page 1: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/1.jpg)
MultiplesIf a number divides exactly into another number, the second is a multiple of the first.
Example3, 6, 9, 12, 15, 18
Example10, 12, 14, 16, 18, 20
are the first six multiples of 3
are the set of multiples of 2 between 10 and 20 inclusive
![Page 2: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/2.jpg)
Example
From the set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Write down the multiples of
(i) 2
(ii) 4
(iii) 6
![Page 3: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/3.jpg)
Lowest Common Multiple (LCM)
Example
Find the lowest common multiple of 12 and 15.
That is the smallest common multiple of the two numbers
![Page 4: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/4.jpg)
Example
Find the lowest common multiple of 9 and 12.
![Page 5: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/5.jpg)
FactorsA factor is a number that will divide exactly into a given number
Example
List all the factors of
(i) 6
(ii) 12
(iii) 30
(iv) 19
![Page 6: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/6.jpg)
Prime numbers
A prime number is a number that can be divided exactly by itself and
one only.
In other words it has only two factors
Example
List the first 8 prime numbers.
![Page 7: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/7.jpg)
Prime Factors
When we want to express a number as a product of its prime factors
we express the number as a multiplication of prime numbers
Example
Express 48 in terms of its prime factors
![Page 8: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/8.jpg)
Example
Express each of the following as products of prime numbers
a) 100
b) 42
c) 72
d) 84
e) 144
![Page 9: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/9.jpg)
Highest common factor (HCF)
The highest common factor of two or more numbers is the greatest
number which will divide exactly into each of them.
Example
Find the HCF of 4, 6 and 8
![Page 10: Multiples If a number divides exactly into another number, the second is a multiple of the first. Example 3, 6, 9, 12, 15, 18 Example 10, 12, 14, 16, 18,](https://reader036.vdocuments.mx/reader036/viewer/2022082817/56649dd15503460f94ac6fd0/html5/thumbnails/10.jpg)
Example
Find the HCF of
a) 6, 9 and 12
b) 12 and 18