How to do long division, step by step, with remainders

Long division repeats four steps until no digits are left: divide, multiply, subtract, then bring down the next digit.

It looks long on paper, but each step is a small calculation that uses the times tables. This guide starts with short division, the bus stop method, then works through a long division one step at a time, explains the three ways to write a remainder, shows how to check an answer, and ends with what the Year 6 tests expect and a set of practice questions with answers.

Short division first: the bus stop method

Short division is the same method with the subtractions done in your head. Pupils meet it before long division: the national curriculum asks Year 4 pupils to practise short division with exact answers, and Year 5 pupils to divide numbers up to 4 digits by a one-digit number using short division and to interpret remainders.

Take 756 ÷ 6. Write 756 under the bar of the bus stop and 6 outside it.

• 6 goes into 7 once, with 1 left over. Write 1 above the 7 and carry the 1 to make 15.
• 6 goes into 15 twice, with 3 left over. Write 2 above the 5 and carry the 3 to make 36.
• 6 goes into 36 exactly 6 times. Write 6 above the last digit.

The answer is 126. When the divisor has two digits, the carried remainders get harder to hold in your head, and that is where long division helps: it writes every subtraction down.

The long division method, step by step

Long division uses four steps, repeated for each digit: divide, multiply, subtract, bring down. Here is 7,128 ÷ 24.

The hardest part is the first estimate at each step. A list of the first multiples of the divisor, written at the side before you start (24, 48, 72, 96, 120, and so on), turns every estimate into a lookup. That list is the times table extended, which is why the multiplication tables from 2 to 12 matter so much here.

Long division with remainders

When the last subtraction does not give 0, the number left is the remainder. In Year 6, the national curriculum asks pupils to interpret remainders in three ways, as appropriate for the context:

• As a whole number remainder. 7,130 ÷ 24 = 297 remainder 2, written 297 r 2.
• As a fraction. The remainder goes over the divisor: 297 2/24, which simplifies to 297 1/12.
• By rounding. As a decimal, 297 1/12 is about 297.08, or 297 to the nearest whole number.

The context decides which one makes sense. If 500 people travel in coaches of 52 seats, 500 ÷ 52 = 9 r 32: nine coaches are not enough, so the answer to the question is 10 coaches. If 500 cm of ribbon is cut into pieces of 52 cm, the answer is 9 pieces, with 32 cm left over.

How to check a division

Every division can be checked with a multiplication. Multiply the answer by the divisor and add the remainder: you should get back the number you started with. For 7,130 ÷ 24 = 297 r 2, the check is 24 × 297 = 7,128, plus 2 makes 7,130.

An estimate before you start catches the biggest errors. 7,130 ÷ 24 is close to 7,000 ÷ 25, which is 280, so an answer near 300 is plausible, while 29 or 2,970 would be a misplaced digit. Rounding the divisor to 25 is useful because dividing by 25 is the same as multiplying by 4 and dividing by 100.

A last quick test: if the divisor is even and the number you divide is odd, the answer cannot be a whole number. It is a good way to spot a missing remainder.

Long division in the Year 6 tests

Long division appears on the arithmetic paper of the key stage 2 tests. The 2026 mathematics mark schemes show how it is marked:

• a correct answer earns 2 marks;
• a formal method with no more than one arithmetic error can still earn 1 mark;
• chunking, subtracting multiples of the divisor, counts as a formal method when the size of each chunk is shown;
• a remainder must be expressed correctly, and an answer such as 25 r 0 or 25.0 is accepted for 25, but 250 is not.

Chunking is worth knowing as a back-up. For 7,128 ÷ 24, subtract 200 lots of 24 (4,800) to leave 2,328, then 90 lots (2,160) to leave 168, then 7 lots (168) to leave 0. The chunks add up to 200 + 90 + 7 = 297. It takes more lines, but each step uses only easy multiples, and the mark scheme accepts it when the chunks are shown.

So showing the working is worth it even when time is short: a slip in one subtraction does not cost both marks. Our guide to the Year 6 maths SATs explains the rest of the papers and the 2027 dates.

Long division practice questions

Try each question on paper, then check with a multiplication. The first two can be done with short division.

For the last question, a decimal answer comes from carrying on past the units: write 5,000 as 5,000.00 and keep dividing. The remainder 8 becomes 80 tenths; 80 ÷ 32 = 2 remainder 16; 160 hundredths ÷ 32 = 5 exactly. The answer is 156.25, which matches 156 1/4.

If a child gets stuck, go back to the list of multiples rather than to the method: most errors in long division are times table errors in disguise. Sitting nearby and asking questions works better than taking the pencil, as our guide to helping with maths homework explains. Kalc trains times tables, fractions, percentages and algebra in about ten minutes a day.

Frequently asked questions

What are the steps of long division?

Divide, multiply, subtract and bring down the next digit, repeated until no digits are left. What remains after the last subtraction is the remainder.

What is the difference between short division and long division?

They follow the same logic. Short division keeps the subtractions in your head, so it suits one-digit divisors; long division writes every subtraction down.

How do you write a remainder in long division?

As a whole number remainder (297 r 2), as a fraction over the divisor (297 2/24, or 297 1/12), or by rounding the decimal answer, depending on the context.

When do children learn long division in England?

In Year 6, the national curriculum asks pupils to divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division.

How do you check a long division answer?

Multiply the answer by the divisor and add the remainder. For 7,130 ÷ 24 = 297 r 2, 24 × 297 + 2 gives back 7,130.