MATHEMATICSTypes of Number – Multiples, Factors & Primes

Aims of the Lesson

• To learn about multiples, factors and prime numbers.

• To extend this into learning about lowest common multiples and highest common factors.

Multiples

• Multiples are the multiplication tables of the number given

• E.g. the multiples of 3 are: 3, 6, 9, 12…

• E.g. the multiples of 25 are 25, 50, 75, 100…

Multiple Tasks

1) Write down the first 10 multiples of 4

2) Write down the first 10 multiples of 5

3) Write down the first 10 multiples of 10

Answers

1) Multiples of 4 = 4 Times table…

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

2) Multiples of 5 = 5 Times table…

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

3) Multiples of 10 = 10 Times table…

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

LCM

• Lowest (ie. smallest value)• Common (that appears in every list)• Multiples (of each values’ multiplication table)

• Given two (or more) numbers you may be asked to find their lowest common multiple (LCM)

LCM Example

• What is the LCM of 6 and 8?

• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48…• Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64…

• The common factors are in blue but the lowest of these is 24

LCM Tasks

• Using your answers from your multiple tasks…

1) What is the LCM of 4 and 5?

2) What is the LCM of 4 and 10?

Answers

1) 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

LCM of 4 and 5 = 20

2) 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

LCM of 4 and 10 = 20

What next?

Work through the MyMaths lesson (and then its online homework) called:Number > Counting & Place Value > Multiples

Work through the MyMaths lesson (and then its online homework) called:Number > Powers and Roots > Lowest Common Multiple

Now move on to ‘factors’ on the next slide…

Factors

• Factors are numbers which divide exactly into a value

• That value can be made by multiplying factors together

• Finding different factor pairs helps find all the factors

Factors Example

• List all the factors of 12.

• Finding the factors of 12 using factor pairs:1 × 12 2 × 6 3 × 4

• All of the above pairs make 12

• The factors of 12 in ascending order are:

1, 2, 3, 4, 6 & 12

Factor Tasks

1) Find all the factors of 20

2) Find all the factors of 30

3) Find all the factors of 32

Answers

1) 20 = 1 × 20, 2 × 10, 4 × 5

Factors of 20 = 1, 2, 4, 5, 10, 20

2) 30 = 1 × 30, 2 × 15, 3 × 10, 5 × 6

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

3) 32 = 1 × 32, 2 × 16, 4 × 8

Factors of 40 = 1, 2, 4, 8, 16, 32

HCF

• Highest (ie. biggest value)• Common (that appears in every list)• Factor (ie. of numbers that divide it exactly)

• Given two (or more) numbers you may be asked to find their highest common factor (HCF)

HCF Example

What is HCF of 24 and 30?

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

•All the ‘common factors’ are in blue, but the highest of these is 6.

HCF Tasks

• Using your answers from your factor tasks…

1) What is the HCF of 20 and 30?

2) What is the HCF of 20 and 32?

Answers

1) Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

HCF of 20 & 30 = 10

2) Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 32: 1, 2, 4, 8, 16, 32

HCF of 20 & 32 = 4

Prime Numbers

• A prime number has exactly two different factors

• It can only be divided exactly by 1 or itself

• 1 is not a prime number – it only has one factor

• 2 is the only even prime number

Prime Examples• Is 7 a prime number?

• YES: Factors are only 1 & 7 (2 factors)

• Is 9 a prime number?• NO: Factors are 1, 3 & 9 (3 factors)

• Is 20 a prime number?• NO: It is an even number!

Prime Numbers 1 - 100

• Printout worksheet: NoSq100.xlsx

• Cross out ‘1’ – it is NOT a prime number as it only has 1 factor (not 2).

• Circle ‘2’ and then cross out EVERY other number in the 2 times table.

• Circle ‘3’ and then cross out EVERY other number in the 3 times table.

• 4 is already crossed out so move on to 5.

Prime Numbers 1 – 100 (cont’d)

• Circle 5 and then cross out EVERY other number in the 5 times table.

• 6 is already crossed out so move on to 7.

• Circle 7 and then cross out EVERY other number in the 7 times table.

• Now circle all the remaining numbers that have not been crossed out.

Check

• You have just found all the prime numbers between 1 and 100.

• You should have ONLY the following numbers circled…

• 2, 3, 5, 7, 11, 13, 17, 19, • 23, 29, 31, 37,• 41, 43, 47, 53, 59,• 61, 67, 71, 73, 79,• 83, 89, 93, 97

What next?

Work through the MyMaths lesson (and then its online homework) called:Number > Counting & Place Value > Factors and Primes

Work through the MyMaths lesson (and then its online homework) called:Number > Powers and Roots > Highest Common Factor

Save and complete the worksheet: LCM-HCF.xlsx