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**Types of Number – Multiples, Factors & Primes**

Mathematics Types of Number – Multiples, Factors & Primes

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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.

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**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…

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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

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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

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**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)

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**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

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**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?

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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

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What next? Work through the MyMaths lesson (and then its online homework) called: Number > Counting & Place Value > Multiples Number > Powers and Roots > Lowest Common Multiple Now move on to ‘factors’ on the next slide…

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**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

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**Factors Example List all the factors of 12.**

Finding the factors of 12 using factor pairs: 1 × × 6 3 × 4 All of the above pairs make 12 The factors of 12 in ascending order are: 1, 2, 3, 4, 6 & 12

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Factor Tasks 1) Find all the factors of 20 2) Find all the factors of 30 3) Find all the factors of 32

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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

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**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)

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**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.

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**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?

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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

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**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

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**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!

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**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.

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**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.

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**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

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What next? Work through the MyMaths lesson (and then its online homework) called: Number > Counting & Place Value > Factors and Primes Number > Powers and Roots > Highest Common Factor Save and complete the worksheet: LCM-HCF.xlsx

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