Highest common factor: Venn diagrams

The Maths Habit

Where does each shape go?

A
B
C
D
4 sidesShadedABC
D: outside both

Is the first number a factor of the second?

4 and 12Yes
5 and 12No
3 and 15Yes

Factor
A number that divides exactly into another number.
Common factor
A factor that two numbers share.
68361248
Highest common factor (HCF)
The biggest factor that two numbers share.
68361248

Factors of 61236
Factors of 81248
68361248
  1. 1List the factors of each number.Use the ladder from last lesson.
  2. 2Put the shared factors in the middle.The rest go in their own circle.

Put the factors of 10 and 12 in the Venn.

1List the factors of each number.
Factors of 1012510
Factors of 121234612
2Put the shared factors in the middle.
10125101234612

Put the factors of 6 and 9 in the Venn.

1List the factors of each number.
Factors of 61236
Factors of 9139
2Put the shared factors in the middle.
6926139

Put the factors of 10 and 12 in the Venn.

1List the factors of each number.
Factors of 1012510
Factors of 121234612
2Put the shared factors in the middle.
10125101234612
1List the factors of each number.2Put the shared factors in the middle.

Put the factors of 4 and 10 in the Venn.

1List the factors of each number.
Factors of 4124
Factors of 1012510
2Put the shared factors in the middle.
410412510

Put the factors of 10 and 12 in the Venn.

1List the factors of each number.
Factors of 1012510
Factors of 121234612
2Put the shared factors in the middle.
10125101234612
1List the factors of each number.2Put the shared factors in the middle.

Put the factors of 12 and 16 in the Venn.

1List the factors of each number.
Factors of 121234612
Factors of 16124816
2Put the shared factors in the middle.
12163612124816

Put the factors of 10 and 12 in the Venn.

1List the factors of each number.
Factors of 1012510
Factors of 121234612
2Put the shared factors in the middle.
10125101234612
1List the factors of each number.2Put the shared factors in the middle.

Put the factors of 10 and 25 in the Venn.

1List the factors of each number.
Factors of 1012510
Factors of 251525
2Put the shared factors in the middle.
10252101525

1List the factors of each number.2Put the shared factors in the middle.

1Put the factors of 4 and 6 in the Venn.

Factors of 4124
Factors of 61236
4641236

2Put the factors of 6 and 15 in the Venn.

Factors of 61236
Factors of 1513515
6152613515

3Put the factors of 18 and 20 in the Venn.

Factors of 181236918
Factors of 2012451020
18203691812451020

Factors of 61236
Factors of 81248
683612248
HCF = 2
  1. 1List the factors of each number.Use the ladder from last lesson.
  2. 2Put the shared factors in the middle.The rest go in their own circle.
  3. 3Ring the biggest in the middle.That is the HCF.

Find the HCF of 18 and 27.

1List the factors of each number.
Factors of 181236918
Factors of 2713927
2Put the shared factors in the middle.
1827261813927
3Ring the biggest in the middle.
HCF = 9

Find the HCF of 20 and 28.

1List the factors of each number.
Factors of 2012451020
Factors of 2812471428
2Put the shared factors in the middle.
20285102012471428
3Ring the biggest in the middle.
HCF = 4

Find the HCF of 18 and 27.

1List the factors of each number.
Factors of 181236918
Factors of 2713927
2Put the shared factors in the middle.
1827261813927
3Ring the biggest in the middle.
HCF = 9
1List the factors of each number.2Put the shared factors in the middle.3Ring the biggest in the middle.

Find the HCF of 15 and 18.

1List the factors of each number.
Factors of 1513515
Factors of 181236918
2Put the shared factors in the middle.
15185151326918
3Ring the biggest in the middle.
HCF = 3

Find the HCF of 18 and 27.

1List the factors of each number.
Factors of 181236918
Factors of 2713927
2Put the shared factors in the middle.
1827261813927
3Ring the biggest in the middle.
HCF = 9
1List the factors of each number.2Put the shared factors in the middle.3Ring the biggest in the middle.

Find the HCF of 6 and 18.

1List the factors of each number.
Factors of 61236
Factors of 181236918
2Put the shared factors in the middle.
6181236918
3Ring the biggest in the middle.
HCF = 6

Find the HCF of 18 and 27.

1List the factors of each number.
Factors of 181236918
Factors of 2713927
2Put the shared factors in the middle.
1827261813927
3Ring the biggest in the middle.
HCF = 9
1List the factors of each number.2Put the shared factors in the middle.3Ring the biggest in the middle.

Find the HCF of 20 and 25.

1List the factors of each number.
Factors of 2012451020
Factors of 251525
2Put the shared factors in the middle.
20252410201525
3Ring the biggest in the middle.
HCF = 5

Highest common factor: Venn diagrams worksheet, page 1

Highest common factor: Venn diagrams worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. The HCF of 6 and 9 is 3

    Right

  2. The HCF of 8 and 12 is 2

    Wrong: the HCF is 4

  3. 1 is a common factor of 7 and 10

    Right

  4. The HCF of 5 and 10 is 10

    Wrong: the HCF is 5

  5. 5 is a common factor of 10 and 12

    Wrong: 5 is not a factor of 12

  1. Find the HCF of 24 and 36.

    12

  2. Find the HCF of 12, 18 and 30.

    6

  3. Two numbers are less than 20. Their HCF is 5. What could they be?

    5 and 10, for example

  1. Find the HCF of 6 and 10.

    2
    1List the factorsof each number.Factors of 61236Factors of 10125103Ring the biggestin the middle.HCF =2Put the sharedfactors in themiddle.610

  2. Find the HCF of 9 and 15.

    3
    1List the factorsof each number.Factors of 9Factors of 153Ring the biggestin the middle.HCF =2Put the sharedfactors in themiddle.915

  3. Find the HCF of 18 and 30.

    6
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