1. Highest Common Factor – Prime Factorisation – Demonstration
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2. Find the Highest Common Factor (HCF) of 12 & 20.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 12 20
Shared Factors 12 20 3 2 6 2 10 5 2 2 2 3 2 5
3) HCF = Product of shared factors
2 × 2
= 4
12 = 2 × 2 × 3
20 = 2 × 2 × 5

3. Find the Highest Common Factor (HCF) of 18 & 45.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 18 45
Shared Factors 18 45 2 2 9 3 15 3 5 3 3 3 3 5
3) HCF = Product of shared factors
3 × 3
= 9
18 = 2 × 3 × 3
45 = 3 × 3 × 5

4. Find the Highest Common Factor (HCF) of 24 & 36.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 24 36
Shared Factors 24 36 2 2 2 12 2 18 2 3 3 2 6 2 9 2 3 3 3
3) HCF = Product of shared factors
2 × 2 × 3
= 12
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3

5. Find the Highest Common Factor (HCF) of 75 & 90.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 75 90
Shared Factors 75 90 2 5 3 25 2 45 3 5 3 5 5 5 9 3 3
3) HCF = Product of shared factors
3 × 5
= 15
75 = 3 × 5 × 5
90 = 2 × 3 × 3 × 5

6. Find the Highest Common Factor (HCF) of 20 & 30.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 30 20 2
20 = 2 × 2 × 5 2 5 3
30 = 2 × 3 × 5
3) HCF = Product of shared factors
2 × 5
= 10

7. Find the Highest Common Factor (HCF) of 18 & 24.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram 24 18 2 2
18 = 2 × 3 × 3 3 3 2
24 = 2 × 2 × 2 × 3
3) HCF = Product of shared factors
2 × 3
= 6

8. Find the Highest Common Factor (HCF) of 120 & 150.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram
150
120 2 5
120 = 2 × 2 × 2 × 3 × 5 2 3 5
150 = 2 × 3 × 5 × 5 2
3) HCF = Product of shared factors
2 × 3 × 5
= 30

9. Find the Highest Common Factor (HCF) of 63 & 210.
1) Complete Prime Factorisation
for both numbers.
2) Input the Prime Factors into a Venn diagram
210 63 2
63 = 3 × 3 × 7 3 3 5
210 = 2 × 3 × 5 × 7 7
3) HCF = Product of shared factors
3 × 7
= 21

10. 1) Complete Prime Factorisation
for both numbers.
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
2) Input the Prime Factors into a Venn diagram 18 24 2 3
3) HCF = Product of shared factors
2 × 3
= 6
Find the Highest Common Factor (HCF)
of these pairs of numbers.
a) 20 & 30
HCF =
a) 54 & 36
a) 80 & 300
b) 12 & 18 & 90
b) 12 & 40
HCF =
b) 80 & 24
c) 80 & 150 & 180
c) 18 & 45
HCF =
c) 90 & 150

11. 1) Complete Prime Factorisation
for both numbers.
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
2) Input the Prime Factors into a Venn diagram 18 24 2 3
3) HCF = Product of shared factors
2 × 3
= 6
Find the Highest Common Factor (HCF)
of these pairs of numbers.
a) 20 & 30
HCF = 10
a) 54 & 36
HCF = 18
a) 80 & 300
HCF = 20
b) 12 & 18 & 90
b) 12 & 40
HCF = 4
b) 80 & 24
HCF = 8
HCF = 6
c) 80 & 150 & 180
c) 18 & 45
HCF = 9
c) 90 & 150
HCF = 30
HCF = 10

12. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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