HCF: the ladder method

The Maths Habit

Work out

14 ÷ 27
24 ÷ 38
35 ÷ 57

Yes or no?

Is 2 a factor
of both 10 and 16?Yes
Is 3 a factor
of both 12 and 20?No
Is 5 a factor
of both 15 and 40?Yes
2: the number is even.3: it is in the 3 times table.5: it ends in 0 or 5.

Factor
A number that divides exactly into another number.
Common factor
A number that is a factor of both numbers.
2101457
Highest common factor (HCF)
The biggest number that is a factor of both numbers.
281224623

Build the ladder for 18 and 30.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
21830391535

Build the ladder for 20 and 28.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
220282101457

Build the ladder for 18 and 30.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
21830391535
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.

Build the ladder for 20 and 24.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
220242101256

Build the ladder for 18 and 30.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
21830391535
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.

Build the ladder for 28 and 36.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
228362141879

Build the ladder for 18 and 30.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
21830391535
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.

Build the ladder for 15 and 25.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
5152535

Find the HCF of 30 and 36.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
230363151856
3Multiply down the side.
HCF =2×3=6

Find the HCF of 40 and 50.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
240505202545
3Multiply down the side.
HCF =2×5=10

Find the HCF of 30 and 36.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
230363151856
3Multiply down the side.
HCF =2×3=6
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.3Multiply down the side.

Find the HCF of 12 and 16.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
2121626834
3Multiply down the side.
HCF =2×2=4

Find the HCF of 30 and 36.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
230363151856
3Multiply down the side.
HCF =2×3=6
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.3Multiply down the side.

Find the HCF of 15 and 20.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
5152034
3Multiply down the side.
HCF =5=5

Find the HCF of 30 and 36.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
230363151856
3Multiply down the side.
HCF =2×3=6
1Divide both by 2, 3 or 5.2Keep going until none of them is a factor of both.3Multiply down the side.

Find the HCF of 16 and 40.

1Divide both by 2, 3 or 5.
2Keep going until none of them is a factor of both.
216402820241025
3Multiply down the side.
HCF =2×2×2=8

HCF: the ladder method worksheet, page 1

HCF: the ladder method worksheet, page 2

Answer sheet

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

  1. The HCF of 10 and 15 is 5

    Right

  2. You can stop the ladder at 4 and 6

    Wrong: 2 is a factor of both

  3. The side is 2 and 5, so the HCF is 7

    Wrong: 2 × 5 = 10

  4. 3 is a factor of both 9 and 20

    Wrong: 3 is not a factor of 20

  5. The HCF of 8 and 28 is 4

    Right

  1. Find the HCF of 42 and 70. You will need to divide by 7 as well.

    14

  2. Find the HCF of 24, 36 and 60. Each number you divide by must be a factor of all three.

    12

  3. Build the ladder for 12 and 18. Multiply the side and the bottom together. This is the LCM. What is it?

    36

  1. Find the HCF of 12 and 28.

    4
    1Divide both by2, 3 or 5.2Keep going untilnone of them is afactor of both.3Multiply downthe side.21228614HCF =×=

  2. Find the HCF of 18 and 42.

    6
    1Divide both by2, 3 or 5.2Keep going untilnone of them is afactor of both.3Multiply downthe side.1842HCF =×=

  3. Find the HCF of 30 and 40.

    10
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