How to do long division

Long division is the written way to divide by a number too big to do in your head. It turns one hard division into a short run of easy ones, each answered from the times table.

The rule

Work from left to right. Divide, multiply, subtract, then bring down the next digit, and repeat until there are no digits left to bring down.

How to do it

Write the number you are dividing (the dividend) under the bar, and the number you are dividing by (the divisor) outside it on the left.
Take the first digit of the dividend, or the first two if the first is too small, and work out how many times the divisor goes into it. Write that above the bar, over the last digit you used.
Multiply that answer by the divisor, write the result underneath, and subtract.
Bring the next digit of the dividend down beside what is left. That is your next number to divide.
Repeat until every digit has come down. Whatever is left at the end is the remainder.

Worked examples

What is 343 ÷ 7?

		4	9
7	3	4	3
−	2	8
		6	3
	−	6	3
			0

7 does not go into 3, so start with 34. 34 ÷ 7 = 4, leaving 6. Bring down the 3 to make 63, and 63 ÷ 7 = 9 exactly. 343 ÷ 7 = 49.

What is 745 ÷ 6?

	1	2	4
6	7	4	5
−	6
	1	4
−	1	2
		2	5
	−	2	4
			1

Something is left after the last digit comes down, so the answer has a remainder: 745 ÷ 6 = 124 remainder 1.

What is 612 ÷ 6?

	1	0	2
6	6	1	2
−	6
		1	2
	−	1	2
			0

After the first step nothing is left, and 6 does not go into the 1 that comes down, so write 0 above it and bring down the 2 as well. 612 ÷ 6 = 102, not 12.

What is 7848 ÷ 24?

		3	2	7
24	7	8	4	8
−	7	2
		6	4
	−	4	8
		1	6	8
	−	1	6	8
				0

With a two-digit divisor the steps are the same; only the times table is harder. 78 ÷ 24 = 3, 64 ÷ 24 = 2, 168 ÷ 24 = 7, so 7848 ÷ 24 = 327.

Short division, the bus stop without the working

Short division is the same method with the multiplying and subtracting done in your head. Instead of writing the subtraction underneath, you write what is left as a small digit in front of the next one: for 745 ÷ 6, 6 into 7 is 1 with 1 left, so a small 1 goes before the 4 to make 14.

It is quicker for a one-digit divisor. With a divisor like 24 the subtractions are too big to hold in your head, which is what long division is for.

Other countries write it differently

The steps are the same everywhere, but the picture is not. Germany writes 7848 : 24 = 327 on one line and works underneath; France, Spain, Italy and most of Latin America put the divisor on the right with the answer under it; Sweden mirrors the bus stop, with the divisor on the right. A child taught one layout can be thrown by another, even though the arithmetic is identical.

Why it works

Each step divides one place value at a time. In 745 ÷ 6, 7 hundreds shared into 6 is 1 hundred each, with 1 hundred left. That hundred is 10 tens, and with the 4 tens already there it makes 14 tens: shared into 6, that is 2 tens each, 2 tens left. Those are 20 ones, and with the 5 ones they make 25, which is 4 each with 1 left over.

Bringing a digit down is that change of unit. Whatever is left over is broken into the next smaller place value and added to what was already there.

To check, multiply back: 124 × 6 + 1 = 745. The answer times the divisor, plus the remainder, always gives the number you started with.

Where mistakes happen

Missing a 0 in the answer. When the divisor does not go into the number you have, write 0 above it before bringing down the next digit. Skipping it is how 612 ÷ 6 comes out as 12.
A remainder as big as the divisor. If what is left after subtracting is the divisor or more, the digit you just wrote above the bar is too small.
Writing an answer digit over the wrong column. It goes above the last digit of the number you just divided, which keeps every digit of the answer in its place.
Forgetting to bring a digit down, or bringing the same one down twice. Tick each digit as it comes down.

Questions people ask

What are the dividend, divisor and quotient?

In 745 ÷ 6 = 124 remainder 1, 745 is the dividend (the number being divided), 6 the divisor (what you divide by), 124 the quotient (the answer) and 1 the remainder.

Is there a way to remember the steps?

Divide, multiply, subtract, bring down. The usual mnemonic has one word for each step, in order: "Does McDonald's Sell Burgers?"

What if the division does not come out exactly?

You can stop with a remainder, or keep going past the decimal point by writing zeros after it, so 127 ÷ 4 is 31 remainder 3, or 31.75. See how to divide decimals.

Why is it called the bus stop?

Because the bracket over the dividend looks like a bus shelter, with the numbers queuing underneath. It is the British name; Americans usually just call it the long division bracket.