Using Prime Factors to Find Highest Common Factor (HCF)
Learn how prime factors are used to find the Highest Common Factor (HCF) of numbers like 80 and 60, along with visual representations and Venn diagrams. Understand the concept with examples and illustrations provided in the content.
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1 2 3 4 5 6 7 8 9 10 11 12 What numbers do the colours represent? What would this model look like for the numbers 13 20? How many additional colours would you need?
On your whiteboard From last lesson Write 80 as a product of its prime factors ? ? ? ? ?
On your whiteboard Use your prime factor tiles to find factors of 80 ? ? ? ? ?
On your whiteboard From last lesson Write 60 as a product of its prime factors ? ? ? ?
On your whiteboard Use your prime factor tiles to find factors of 80 ? ? ? ?
80 = 2 x 2 x 2 x 2 x 5 60 = 2 x 2 x 2 x 3 x 5 Prime factors can be used to find the HCF of both 80 and 60. The largest factor of 80 is all of the prime factors multiplied together 2 x 2 x 2 x 2 x 5 which is 80. 60 doesn t have all of the same prime factors so 80 isn t a factor of 60. What is the biggest factor we can make that can be made by BOTH sets of prime factors?
This circle contains the prime factors of 60 ? ? ? ?
This circle contains the prime factors of 80 ? ? ? ?
This circle contains the prime factors of 60 This circle contains the prime factors of 80 ? ? ? ? ? ? ? ? ?
This circle still contains the prime factors of 60 This circle still contains the prime factors of 80 ? ? ? ? ? ?
By using a Venn Diagram it can be seen that the HCF of 60 and 80 is 2 2 5 = ?? ? ? ? ? ? ?
Find the Highest Common Factor (HCF) of 18 & 45. Shared Factors 45 18 45 18 2 3 15 2 9 5 3 3 3 5 3 3 HCF = Product of shared factors 3 3 = 9 18 = 2 3 3 45 = 3 3 5
Find the Highest Common Factor (HCF) of 24 & 36. Shared Factors 36 24 36 24 2 2 2 18 3 2 12 2 3 2 9 2 6 3 3 2 3 HCF = Product of shared factors 2 2 3 = 12 24 = 2 2 2 3 36 = 2 2 3 3
Find the Highest Common Factor (HCF) of 75 & 90. Complete Prime Factorisation for both numbers. Input the Prime Factors into a Venn diagram Shared Factors 90 75 90 75 2 5 2 45 3 3 25 3 5 5 9 5 5 3 3 HCF = Product of shared factors 3 5 = 15 75 = 3 5 5 90 = 2 3 3 5
100 = 2 x 2 x 5 x 5 75 = 3 x 5 x 5 180 = 2 x 2 x 3 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 150 = 2 x 3 x 5 x 5 Title: Using Prime Factors to work out the HCF Find the HCF of 100 and 120. Find the HCF of 120 and 180. Find the HCF of 150 and 180. Find the HCF of 150 and 75. Find the HCF of 100 and 180.
100 = 2 x 2 x 5 x 5 75 = 3 x 5 x 5 180 = 2 x 2 x 3 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 150 = 2 x 3 x 5 x 5 Find the HCF of 100 and 120 = 20. Find the HCF of 120 and 180 = 60 Find the HCF of 150 and 180 = 30 Mark your work Find the HCF of 150 and 75 = 75 Find the HCF of 100 and 180 = 20
18 = 2 3 3 1) Complete Prime Factorisation for both numbers. 24 = 2 2 2 3 24 18 2 2 2) Input the Prime Factors into a Venn diagram 3 3 2 2 3 3) HCF = Product of shared factors = 6 Find the Highest Common Factor (HCF) of these pairs of numbers. a) 20 & 30 a) 54 & 36 a) 80 & 300 HCF = b) 12 & 18 & 90 b) 12 & 40 b) 80 & 24 HCF = c) 80 & 150 & 180 c) 18 & 45 c) 90 & 150 HCF =
18 = 2 3 3 1) Complete Prime Factorisation for both numbers. 24 = 2 2 2 3 24 18 2 2 2) Input the Prime Factors into a Venn diagram 3 3 2 2 3 3) HCF = Product of shared factors = 6 Find the Highest Common Factor (HCF) of these pairs of numbers. a) 20 & 30 a) 54 & 36 a) 80 & 300 HCF = 20 HCF = 10 HCF = 18 b) 12 & 18 & 90 HCF = 6 b) 12 & 40 b) 80 & 24 HCF = 4 HCF = 8 c) 80 & 150 & 180 HCF = 10 c) 18 & 45 c) 90 & 150 HCF = 30 HCF = 9
Challenge How many factors do factorial numbers have? 1! = 1 .(1 ??????) 2! = 2 1 = 2 .(2 ???????) 3! = 3 2 1 = 6 .(4 ???????) 4! = 4 3 2 1 = 24 . 8 ??????? How many factors does 5! have? What about 6! ?
