Year 6 · Arithmetic skills · Skill 6C

Skill 6C: Long division with no remainders

Use the formal written method to divide 4-digit numbers by 2-digit numbers exactly.

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Worked examples

Long division is for dividing by a 2-digit number. Write out the multiples of the divisor first, then divide in stages: find the biggest multiple that fits, subtract, and bring down the next digit.

Example 1

A 4-digit number divided by 52

2,184 ÷ 52

Write out the multiples of 52 first. They make every step quicker.
52 × 1 = 5252 × 2 = 10452 × 3 = 15652 × 4 = 20852 × 5 = 26052 × 6 = 31252 × 7 = 36452 × 8 = 41652 × 9 = 468
Set out the division, then work from the left. At each step, find the biggest multiple of the divisor that fits, subtract it, and bring down the next digit.
```
           4 2
52 )   2 1 8 4
     − 2 0 8
     - - - -
         1 0 4
       − 1 0 4
       - - - -
             0
```
1. 218 ÷ 52: 52 × 4 = 208, which is the biggest multiple that fits. 218 − 208 = 10.
2. 104 ÷ 52: 52 × 2 = 104, which is the biggest multiple that fits. 104 − 104 = 0.
Nothing is left over, so 2,184 ÷ 52 = 42. Check: 42 × 52 = 2,184.

Answer: 42

Example 2

A zero in the answer

7,106 ÷ 34

Write out the multiples of 34 first. They make every step quicker.
34 × 1 = 3434 × 2 = 6834 × 3 = 10234 × 4 = 13634 × 5 = 17034 × 6 = 20434 × 7 = 23834 × 8 = 27234 × 9 = 306

Set out the division, then work from the left. At each step, find the biggest multiple of the divisor that fits, subtract it, and bring down the next digit.

         2 0 9
34 )   7 1 0 6
     − 6 8
     - - -
         3 0
         − 0
         - -
         3 0 6
       − 3 0 6
       - - - -
             0

1. 71 ÷ 34: 34 × 2 = 68, which is the biggest multiple that fits. 71 − 68 = 3.
2. 30 ÷ 34: 34 × 0 = 0, which is the biggest multiple that fits. 30 − 0 = 30.
3. 306 ÷ 34: 34 × 9 = 306, which is the biggest multiple that fits. 306 − 306 = 0.
Nothing is left over, so 7,106 ÷ 34 = 209. Check: 209 × 34 = 7,106.

Answer: 209

Top tips

Build a list of multiples of the divisor before you start.
If the amount left is bigger than the divisor, your multiple was too small.
Check by multiplying the answer by the divisor.

Watch out for

Choosing a multiple that is too big and having to start the step again.
Forgetting to write a 0 in the answer when the divisor does not fit.

Try some questions

These are from the worksheet. Work each one out, then open it to check.

1,872 ÷ 24 =

Show the answer
78
3,024 ÷ 36 =

Show the answer
84
4,218 ÷ 57 =

Show the answer
74
6,216 ÷ 84 =

Show the answer
74

All arithmetic skills

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