Long Division Calculator
Perform and display long division with step-by-step working shown.
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About
Long Division Calculator
Enter a divisor and a dividend and the calculator lays the division out the way it is written by hand, with each subtraction lined up under the digit it belongs to. It reports the answer four ways: with a remainder, as a mixed number, as a decimal, and as a check you can verify yourself. Set decimal places above zero and the working carries on past the decimal point instead of stopping.
The parts of a division
Three words cover the whole thing. The dividend is the number being divided, the divisor is the number you are dividing by, and the quotient is the answer. In 8 ÷ 4 = 2, the dividend is 8, the divisor is 4 and the quotient is 2.
A useful way to hold on to it: the dividend is how many objects you have, the divisor is how many groups you want, and the quotient is how many end up in each group. Eight people split into 4 groups gives 2 per group.
The same division can be written three ways, and they all mean the same thing:
When it does not divide evenly
Nine cannot be split into 4 equal whole groups. Since 4 × 2 = 8, nine divided by 4 is 2 with 1 left over, written 2 R1. That leftover is the remainder.
This is a formal result, not a convention. For any whole number a and any positive whole number b there is exactly one pair of whole numbers q and r with
a = b × q + r, where 0 ≤ r < b
which is why the calculator prints a check line. For 100 ÷ 7 it reads 7 × 14 + 2 = 100. If that does not come back to the dividend, the working has gone wrong somewhere, and it is the fastest way to catch it.
The remainder is always smaller than the divisor. If you finish a step with a remainder of 9 while dividing by 7, the quotient digit above it is too small and 7 will go in at least once more. That single rule catches most long division mistakes.
How to do long division
Write the dividend under the bracket with the divisor to its left, then work left to right. Take 100 ÷ 7:
- Divide the first digit by the divisor. 7 does not go into 1, so the first quotient digit is 0 and nothing is written above.
- Take the first two digits together. 7 goes into 10 once, so write 1 above the second digit and 7 underneath.
- Subtract and bring the next digit down. 10 − 7 = 3, and bringing down the 0 makes 30.
- Divide again. 7 goes into 30 four times, so write 4 above the last digit and 28 underneath. 30 − 28 = 2.
There is nothing left to bring down, so the answer is 14 with a remainder of 2. That is where the calculator stops when decimal places are set to 0, and it is what the tableau above shows.
Carrying on past the decimal point
A remainder is only one way to finish. To keep going, put a decimal point after the quotient, add a zero to the remainder, and repeat the same step. The 2 left over becomes 20, and 7 goes into 20 twice with 6 left over, so the quotient continues 14.2. Raise the decimal places control above the calculator and the working extends to show exactly this.
Some divisions stop on their own and some never do. It depends only on the divisor once the fraction has been reduced: if its only prime factors are 2s and 5s, the decimal terminates, because 10 is 2 × 5 and the fraction can be scaled to a power of ten. Any other factor repeats forever.
100 ÷ 7 has a 7 in the divisor, so it repeats. The repeating block is 285714, six digits long, and 14.285714285714 is a rounded reading rather than the exact value. The exact value is the mixed number 14 and 2/7. Our Fraction Calculator covers the conversion in both directions.
Repeat lengths are worth knowing about. Dividing by 7 gives a six-digit repeat, which is the longest possible for a divisor of 7, since the remainders can only take the values 1 to 6 before one has to come round again. That upper bound of one less than the divisor is why 1/3 repeats after one digit while 1/7 takes six.
Why the method works
Long division is repeated subtraction organised by place value. Dividing 100 by 7 is really asking how many 70s fit into 100, then how many 7s fit into what is left. The first quotient digit sits in the tens column because it counts tens of sevens, and writing 7 under the 10 is shorthand for subtracting 70 from 100.
That is why the alignment matters and why a digit written one column out throws the whole answer off by a factor of ten. The columns are carrying the place value, and the calculator above lines every subtraction up under the digit that produced it for exactly that reason.
Short division and chunking
When the divisor is small, most people use short division, carrying the remainder in their head and writing only the quotient. It is the same arithmetic with the working left out, and it is quick for single-digit divisors. Long division exists for the cases where you cannot hold the remainders in your head.
Some schools teach partial quotients, sometimes called chunking. Instead of finding the exact digit each time, you subtract any convenient multiple and keep a running tally: take 10 sevens off 100 to leave 30, then 4 more sevens to leave 2, giving 10 + 4 = 14. It takes more lines but it is harder to get badly wrong, and it makes the repeated-subtraction idea visible.
Notation is not universal
The symbol has a name. It is the long division symbol, sometimes called the division bracket, and the horizontal line running over the dividend is the vinculum. It is drawn as one stroke rather than a parenthesis followed by a separate line, which is why the curve and the bar meet at a point. Unicode encodes it at U+27CC, although few fonts carry the glyph.
The bracket layout on this page is the standard in the United States. In the United Kingdom the same method is often set out as the "bus stop", which looks similar but places the quotient above a line drawn over the dividend. In much of continental Europe and Latin America the divisor is written to the right of the dividend with the quotient beneath it, and in parts of Eastern Europe the working runs in a different order again.
The arithmetic is identical everywhere. Only the furniture moves, which is worth knowing if you are checking a child's homework against a method you were taught somewhere else.
Negative numbers and the remainder
Long division is worked on the sizes of the numbers, and the sign is applied at the end: a negative dividend or a negative divisor gives a negative quotient, and two negatives give a positive one. The calculator above does the working on the magnitudes and says so when a sign is involved.
Remainders with negative numbers are less settled than they look. Mathematicians usually want the remainder to be positive, so −7 divided by 3 is −3 with a remainder of 2. Many programming languages instead truncate toward zero and give −2 remainder −1. Python follows the first convention and C, Java and JavaScript follow the second, so the same expression returns different answers in different languages. If you are checking code against hand arithmetic, that is usually where the disagreement is coming from.
Dividing by zero
There is no answer to 3 ÷ 0. Division asks what number multiplied by the divisor gives the dividend, and nothing multiplied by 0 gives 3. It is undefined rather than infinite, and the calculator returns a message instead of a figure.
Where long division still earns its place
Calculators handle the arithmetic, so the reason to know the method is that it shows you things a decimal answer hides. It tells you the exact remainder rather than a rounded tail, which is what you want when the leftover is a real thing: 100 chairs into vans that hold 7 is 14 full vans and 2 chairs still on the floor, and 14.29 vans is not a useful answer.
It also explains why a repeating decimal repeats, since the remainders visibly start cycling. The same algorithm extends to polynomial long division in algebra, where the setup is the identical bracket and the same divide, multiply, subtract, bring down loop. Learning it once on numbers is what makes that later step read as familiar.
Reading your result
Use the remainder form when the leftover has to stay whole. Use the mixed number when you want the exact value in one figure, since 14 and 2/7 is precise where 14.285714285714 is rounded. Use the decimal when you are feeding the number into something else. The check line at the bottom of the panel multiplies back and adds the remainder, and it should always return your dividend.
Common questions
Frequently asked questions
The dividend is the number being divided, the divisor is the number you divide by, and the quotient is the answer. In 100 divided by 7, the dividend is 100, the divisor is 7 and the quotient is 14, with 2 left over as the remainder.
Multiply the divisor by the quotient and add the remainder. It should give you back the dividend exactly: 7 x 14 + 2 = 100. The calculator prints this check line, and if it does not come back to your starting number then a step has gone wrong.
R marks the remainder, the amount left over once the divisor will not go in a whole number of times any more. 100 divided by 7 is written 14 R2, meaning 7 goes in 14 times with 2 left over. The remainder is always smaller than the divisor.
Put a decimal point after the quotient, add a zero to the remainder, and carry on with the same steps. The remainder of 2 becomes 20, 7 goes into it twice, and the quotient continues as 14.2. Set the decimal places control above zero and the working shows it.
Because 7 is not built from 2s and 5s. A decimal terminates only when the reduced divisor has 2 and 5 as its only prime factors, since 10 is 2 x 5. Dividing by 7 repeats the block 285714 forever, so 14.285714285714 is rounded and the exact answer is the mixed number 14 and 2/7.
They are the same arithmetic. Short division keeps the remainders in your head and writes only the quotient, which works well for single-digit divisors. Long division writes every subtraction down, which is what makes larger divisors manageable.
The working is done on the sizes of the numbers and the sign is applied at the end, so one negative gives a negative quotient and two give a positive one. Remainders are less settled: Python reports -7 divided by 3 as -3 remainder 2, while C, Java and JavaScript give -2 remainder -1.
Division asks what number multiplied by the divisor gives the dividend, and no number multiplied by 0 gives 3. There is no answer, so 3 divided by 0 is undefined rather than infinite, and the calculator returns a message instead of a figure.