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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, 20
are the first six multiples of 3
are the set of multiples of 2 between
10 and 20 inclusive
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
Lowest Common Multiple (LCM)
Example
Find the lowest common multiple of 12 and 15.
That is the smallest common multiple of the two numbers
Example
Find the lowest common multiple of 9 and 12.
Factors
A 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
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.
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
Example
Express each of the following as products of prime numbers
a) 100
b) 42
c) 72
d) 84
e) 144
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
Example
Find the HCF of
a) 6, 9 and 12
b) 12 and 18