Highest Common Factors Highest Common Factors & Lowest common & Lowest common

MultiplesMultiples

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MultiplesMultiples What is a multiple?What is a multiple?

A number that may be divided by another number with no remainder: 4, 6, and 12 are multiples of 2.

i.e. Multiples of 3 are all those numbers which appear in the 3 times table

What are common multiples?What are common multiples?A common multiple of two or more numbers contains each of them a number of times exactly, so, 24 is a common multiple of 3 and 4.

i.e. A number which appears in the times tables of all the numbers you are considering

Lowest Common MultiplesLowest Common Multiples What do we mean by ‘lowest What do we mean by ‘lowest

common multiple’?common multiple’?The smallest multiple that is exactly divisible by every member of a set of numbers.

i.e. the lowest common multiple of 12 and 18 is 36

How can we find lowest common How can we find lowest common multiples?multiples?Write out the first few multiples of all the numbers in the data set

Look for the lowest number that appears in all the lists

Finding Lowest common multiplesFinding Lowest common multiples

Example:Example:Find the lowest common multiple of 3

and 7..First few multiples of 3:

3 6 9 12 15 18 21

First few multiples of 7:

7 14 21

The lowest common multiple of 3 and 7 is:

2121

LOWEST COMMON MULTIPLESLOWEST COMMON MULTIPLES

Find the lowest common multiples for the following sets of numbers:

5 and 7 6 and 10 4, 6, and 12

LCM = 35 LCM = 30 LCM = 24

FactorsFactors

What is a factor?What is a factor?

Factors of a number are those numbers that divide into it exactly with no remainder.

*What are common factors?What are common factors?

I.e. the factors of 12 are 1, 12, 2, 6, 3 and 4.

Common factors are those factors which divide exactly into all the numbers in the set.

Highest Common FactorsHighest Common Factors

What do we mean by highest What do we mean by highest common factor?common factor?

The highest common factor of a data set is the largest number that divides exactly into all the numbers.

*How can we find highest common How can we find highest common factors?factors?

List the first few factors of each number

Look for the highest number that appears in all lists.

Finding Highest Common Finding Highest Common FactorsFactors

ExampleExampleFind the highest common factor of 12 and 15.

The factors of 12 are:

1, 2, 3, 4, 6, and 12

The factors of 15 are:

1, 3, 5, 15

So the highest common factor of 12 and 15 is

33

Highest common factorsHighest common factors Find the highest common factors of Find the highest common factors of

the following sets of numbers.the following sets of numbers.

20 and 30

HCF = 10

14 and 12

HCF = 2

24, 36, and 42

HCF = 6

40, 45 and 50

HCF = 5

Prime FactorsPrime Factors

Sometimes we want to find just the Sometimes we want to find just the prime factors of two numbers.prime factors of two numbers.

What is a prime number?

A prime number only has 2 factors and those 2 factors must be 1 and the number itself.

The first 5 prime numbers are:

2, 3, 5, 7, and 11