Highest common factor: Venn diagrams

The Maths Habit Handout to print

  1. Write 36 as a product of prime factors.

    22 × 32

  2. Write 60 as a product of prime factors.

    22 × 3 × 5

  3. Which number is 22 × 3 × 7?

    84

Which numbers divide into both 12 and 18? How many can you find?

1, 2, 3 and 6

Common factor
A factor that two numbers share.
Highest common factor
The biggest factor that two numbers share.

12 = 2 × 2 × 3
18 = 2 × 3 × 3

Which prime factors do they share?

2 and 3

What is the HCF?

6

Find the HCF of 24 and 40

24 =2 × 2 × 2 × 3
40 =2 × 2 × 2 × 5
HCF2 × 2 × 2 = 8

Find the HCF of 18 and 30

18 =2 × 3 × 3
30 =2 × 3 × 5
HCF2 × 3 = 6

Find the HCF of 24 and 40

24 =2 × 2 × 2 × 3
40 =2 × 2 × 2 × 5
HCF2 × 2 × 2 = 8

Find the HCF of 28 and 70

28 =2 × 2 × 7
70 =2 × 5 × 7
HCF2 × 7 = 14

Find the HCF of 24 and 40

24 =2 × 2 × 2 × 3
40 =2 × 2 × 2 × 5
HCF2 × 2 × 2 = 8

Find the HCF of 20 and 50

20 =2 × 2 × 5
50 =2 × 5 × 5
HCF2 × 5 = 10

Find the HCF of 24 and 40

24 =2 × 2 × 2 × 3
40 =2 × 2 × 2 × 5
HCF2 × 2 × 2 = 8

Find the HCF of 42 and 63

42 =2 × 3 × 7
63 =3 × 3 × 7
HCF3 × 7 = 21

Find the HCF of 24 and 40

24 =2 × 2 × 2 × 3
40 =2 × 2 × 2 × 5
HCF2 × 2 × 2 = 8

Find the HCF of 18 and 54

18 =2 × 3 × 3
54 =2 × 3 × 3 × 3
HCF2 × 3 × 3 = 18

HCF and LCM worksheet, page 1

HCF and LCM worksheet, page 2

Answer sheet

  1. A floor is 180 cm long and 120 cm wide. It is covered with square tiles, with none cut. What is the largest tile that will fit?

    60 cm

  2. Two numbers have a highest common factor of 6. What could they be?

    12 and 18, for example

  1. Find the HCF of 20 and 32.

    4

  2. Find the HCF of 36 and 90.

    18

  3. Strips of card 56 cm and 84 cm long are cut into equal pieces with none left over. What is the longest each piece can be?

    28 cm
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