• Key Stage 2 • Maths
Long division is the formal written method for dividing by a two-digit number. Pupils learn it in Year 6 and it appears in the KS2 arithmetic paper every year. This guide explains the method step by step, with worked examples, practice questions and answers.
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The Quick Answer
- Long division is a written method for dividing a number by a two-digit number, such as 432 ÷ 15.
- It repeats four steps: divide, multiply, subtract and bring down.
- In Year 6, pupils divide numbers up to 4 digits by a two-digit whole number.
- Remainders can be written as a whole number remainder, a fraction or a decimal, or rounded to suit the context.
What Is Long Division?
The Year 6 national curriculum says pupils should divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division. They should interpret remainders as whole number remainders, fractions or by rounding, as appropriate for the context.
In long division you write out each step in full: the multiplication and the subtraction appear under the number being divided. This makes it easier to divide by larger numbers than with short division, where the multiplication and subtraction are done mentally.
How to Do Long Division
Follow the same four steps for each digit:
- Divide: how many times does the divisor go into the first part of the number?
- Multiply: multiply the divisor by that answer and write it underneath.
- Subtract: take it away to find what is left over.
- Bring down: bring down the next digit and repeat.
Tip: before you start, write out the first few multiples of the divisor. For 15 that is 15, 30, 45, 60, 75, 90, 105, 120 and 135. It makes every “divide” step quicker and more accurate.
Worked Example: 7,335 ÷ 15
| Step | Working | Result |
|---|---|---|
| 1 | 15 goes into 7 zero times, so look at 73 | |
| 2 | 15 goes into 73 four times: 4 × 15 = 60 | 73 − 60 = 13 |
| 3 | Bring down the 3 to make 133 | |
| 4 | 15 goes into 133 eight times: 8 × 15 = 120 | 133 − 120 = 13 |
| 5 | Bring down the 5 to make 135 | |
| 6 | 15 goes into 135 nine times: 9 × 15 = 135 | 135 − 135 = 0 |
Answer: 7,335 ÷ 15 = 489. Check it with the inverse: 489 × 15 = 7,335.
Worked Example with a Remainder: 432 ÷ 15
| Step | Working | Result |
|---|---|---|
| 1 | 15 goes into 4 zero times, so look at 43 | |
| 2 | 15 goes into 43 twice: 2 × 15 = 30 | 43 − 30 = 13 |
| 3 | Bring down the 2 to make 132 | |
| 4 | 15 goes into 132 eight times: 8 × 15 = 120 | 132 − 120 = 12 |
The answer is 28 remainder 12. This example comes from Mathematics Appendix 1 of the national curriculum, which shows the remainder written three ways:
| Form | Answer |
|---|---|
| Whole number remainder | 28 r 12 |
| Fraction | 28 12/15 = 28 4/5 |
| Decimal | 28.8 |
Remainders in Word Problems
In a word problem, the context tells you what to do with the remainder. For example, 1,250 pupils are going on a trip and each coach holds 52 pupils. 1,250 ÷ 52 = 24 r 2, so 25 coaches are needed: rounding down would leave 2 pupils behind.
Long Division Practice Questions
- 672 ÷ 12
- 936 ÷ 24
- 845 ÷ 13
- 1,512 ÷ 14
- 2,808 ÷ 36
- 4,725 ÷ 25
- 5,568 ÷ 32
- 6,431 ÷ 59
Show the answers
- 56
- 39
- 65
- 108
- 78
- 189
- 174
- 109
These questions have remainders. Give each answer as a fraction in its simplest form:
- 500 ÷ 16
- 1,000 ÷ 24
- 3,250 ÷ 18
- 2,000 ÷ 35
Show the answers
- 31 r 4 = 31 1/4 (or 31.25)
- 41 r 16 = 41 2/3
- 180 r 10 = 180 5/9
- 57 r 5 = 57 1/7
Long Division in the KS2 Arithmetic Paper
Long division questions in the KS2 arithmetic paper are worth 2 marks. The mark schemes show that if the final answer is wrong, pupils can still get 1 mark for using the formal method of long division with no more than one arithmetic error. Working must be written under the question to count.
When an answer is not a whole number, the remainder must be written correctly. For example, if a pupil divides by 28 and gets 6 r 14, the mark schemes accept 6 14/28 or 6.5, but not 6.14.
Practise the full paper with our Year 6 arithmetic questions and the official Year 6 SATs papers.
Common Mistakes
- Forgetting a zero in the answer: if the divisor does not go into the number after bringing down, write 0 in the answer before bringing down the next digit.
- Leaving a remainder that is too big: a remainder must be smaller than the divisor. If it is not, the divide step needs a bigger number.
- Writing the remainder as a decimal digit: 6 r 14 is not 6.14.
- Misaligning digits: keep each column in line so the bring-down step uses the right digit.
Frequently Asked Questions
What year do children learn long division?
Long division is in the Year 6 national curriculum. Pupils learn short division by a one-digit number in Year 5.
What are the steps of long division?
Divide, multiply, subtract and bring down, repeated for each digit.
What is the difference between short and long division?
In long division the multiplication and subtraction are written out under the number being divided. In short division the multiplication and subtraction are done mentally and only the remainders are written down.
Is chunking accepted in the KS2 arithmetic test?
The mark schemes accept chunking as a formal method only when the chunks are all of different sizes and are shown alongside the working.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study, including Mathematics Appendix 1; Standards and Testing Agency, 2025 KS2 mathematics test mark schemes. Practice questions written by Monster Learning.
