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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

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Multiples
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

2

4

6


Lowest common multiple lcm
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
Factors

A factor is a number that will divide exactly into a given number

Example

List all the factors of

6

12

30

19


Prime numbers
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

Prime Factors


Example factors we express the number as a multiplication of prime numbers

Express each of the following as products of prime numbers

100

42

72

84

144


Highest common factor hcf
Highest common factor (HCF) factors we express the number as a multiplication of prime numbers

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 factors we express the number as a multiplication of prime numbers

Find the HCF of

6, 9 and 12

12 and 18


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