Long Division Calculator
This long division calculator divides one whole number by another and prints the working in the traditional layout — quotient along the top, each product subtracted, the next digit brought down. You also get the remainder, the exact decimal and the fraction form.
How to use the long division calculator
- Type the dividend, the number being divided, into the first box.
- Type the divisor, the number you are dividing by, into the second.
- Choose how far to take it: a number of decimal places, or stop at the remainder to keep the answer as a whole number with a leftover.
- Read the layout in the middle of the results. It is the same arrangement you would write by hand, in a fixed-width font so the columns line up.
- Below it you get the quotient, the whole-number answer with its remainder, the exact decimal, the fraction form and a numbered step list naming the digit position each step is working on.
Everything redraws as you type. Enter a decimal in either box and you get a message rather than a layout, because the paper method needs whole numbers — shift both numbers by the same power of ten first, which is covered below. Very large numbers are turned away too; send those to the division calculator, which is not tied to a printed layout.
The words and the layout
Four words describe the four numbers on the page. The dividend is the number being cut up and it goes inside the bracket. The divisor is the number you are cutting by and it sits outside, on the left. The quotient is the answer, written along the top so each of its digits sits directly above the digit of the dividend it came from. The remainder is whatever is left at the bottom when you stop.
Column position is the whole point. A quotient digit is worth only what its column says: write a 5 one place too far left and you have claimed fifty. That is why the working uses a fixed-width font and why zeros in the quotient are never skipped.
Underneath the dividend, each product is written out, ruled off with a line, and subtracted from the value above it. The next digit of the dividend then drops down onto that result, and the cycle starts again on the new number.
Divide, multiply, subtract, bring down
Long division is one four-step cycle repeated once per digit. Nothing else happens.
- Divide. How many whole times does the divisor go into the number you are holding? That count is the next digit of the quotient.
- Multiply. Multiply the divisor by that digit and write the product underneath.
- Subtract. Take the product away from the number above it. The result must be smaller than the divisor. If it is not, your digit was too small.
- Bring down. Pull the next digit of the dividend down beside that result to make the number you hold for the next cycle.
When the divisor does not fit into the first digit of the dividend, the answer for that column is zero. You have two choices, and both are correct: write the 0 in the quotient and carry on, or absorb it by taking the first two digits together and starting the answer one column further right. Dividing 952 by 28, the 28 does not go into 9 at all, so the first real digit of the quotient sits above the 5.
Example: 952 ÷ 28
952 ÷ 28 = 34, with nothing left over. Check it backwards: 28 × 34 = 952.
A worked example with a two-digit divisor
Two-digit divisors are the case that trips people up, because you can no longer read the answer off a times table. The fix is to estimate, then correct.
Example: 8,536 ÷ 24
Round the divisor to 25 in your head. 25 goes into 85 about three times, so try 3.
So 8,536 ÷ 24 = 355 remainder 16. The check works: 24 × 355 = 8,520, and 8,520 + 16 = 8,536.
The estimate is allowed to be wrong. If the subtraction leaves a number bigger than the divisor, the digit was too low, so raise it by one and redo the line. If it goes negative, the digit was too high. Correcting is part of the method, not a mistake.
Writing out the first few multiples of the divisor before you start removes most of the guessing. For 24: 24, 48, 72, 96, 120, 144, 168, 192, 216. Every step then means finding which of those nine numbers sits just below the value you hold. The multiplication calculator will lay that list out.
Carrying on past the decimal point
A remainder means the division is not finished, only paused. To keep going, put a decimal point in the quotient directly above the one in the dividend, then append zeros to the dividend and keep bringing them down. Adding zeros after a decimal point does not change the value of the number, so nothing has been altered.
Example: taking 8,536 ÷ 24 into decimals
The whole-number part stopped at 355 remainder 16. Now write 8,536 as 8,536.000 and carry on.
The remainder 16 has come back, so the same step will repeat forever: 8,536 ÷ 24 = 355.6666…, written 355.6 with a bar over the 6. As a fraction it simplifies to 1067/3, and the leftover 16/24 is 2/3.
Knowing when to stop is a matter of watching the remainders, not the digits. Every remainder is smaller than the divisor, so dividing by 24 can only ever produce the remainders 0 to 23. Either you hit 0 and the decimal terminates, or a remainder you have already seen comes round again, and from that point the digits between the two sightings repeat forever. That is why the longest possible repeating block is one shorter than the divisor: sevenths repeat in blocks of six.
Set the decimal places to stop at the remainder when you are dividing countable things — 100 pencils into boxes of 12 is 8 full boxes and 4 left over, and 8.33 boxes is not a useful answer. The remainder calculator reports just that leftover, negative numbers included.
| Division | Quotient | Remainder | Decimal |
|---|---|---|---|
| 8,536 ÷ 24 | 355 | 16 | 355.6666… (recurs) |
| 4,832 ÷ 16 | 302 | 0 | 302 |
| 952 ÷ 28 | 34 | 0 | 34 |
| 500 ÷ 32 | 15 | 20 | 15.625 |
| 245 ÷ 11 | 22 | 3 | 22.2727… (recurs) |
| 1,000 ÷ 7 | 142 | 6 | 142.857142… (recurs) |
| 7 ÷ 12 | 0 | 7 | 0.58333… (recurs) |
Read any row across and the three answers say the same thing. 500 ÷ 32 is 15 remainder 20, and that leftover 20/32 is 5/8, which is 0.625 — the tail of the decimal answer. If you want that last conversion on its own, the fraction to decimal calculator does it and marks any repeating block.
Dividing when one number is a decimal
The layout only works with whole numbers, so a decimal in either box gets a message instead of a diagram. Convert the problem first. Multiply both numbers by the same power of ten until neither has a decimal point. The quotient does not change, because scaling both sides of a division equally leaves the ratio alone.
Count the decimal places in whichever number has more, and shift both by that many places, padding with zeros where you run out of digits. Doing it to only one number is the classic error: 15.6 ÷ 24 is 0.65, a hundred times off the real answer.
Common mistakes
- Dropping a zero from the quotient. If the divisor will not go into the current number, the digit is 0 and it still takes up a column. Losing it turns 302 into 32.
- Misaligning the columns. Each quotient digit belongs above the dividend digit that produced it. A single column of drift multiplies or divides the answer by ten.
- Forgetting to bring a digit down. Every digit of the dividend is used, in order, zeros included.
- Leaving a subtraction result bigger than the divisor. That is proof the quotient digit was too small. Increase it by one and redo the line.
- Shifting only one number when the divisor is a decimal. Both numbers move the same number of places, or the answer is out by a power of ten.
- Writing 355.16 for 355 remainder 16. A remainder is not decimal digits. The remainder 16 over the divisor 24 is 2/3, so the decimal is 355.666…
- Rounding a recurring decimal before the end. If the answer feeds into more arithmetic, keep the fraction and round once, at the finish.
Frequently asked questions
What is 8,536 divided by 24?
8,536 ÷ 24 = 355 remainder 16, or 355.6666… as a decimal. The working runs 24 into 85 three times with 13 left, then 24 into 133 five times with 13 left, then 24 into 136 five times with 16 left. As a fraction it is 1067/3. Check it with 24 × 355 + 16 = 8,536.
What is 952 divided by 28?
952 ÷ 28 = 34 exactly. Because 28 does not fit into 9, the first quotient digit sits above the 5: 28 into 95 goes 3 times with 11 left, then bringing down the 2 gives 112, and 28 goes into 112 exactly 4 times. Nothing is left over, and 28 × 34 = 952.
What are the four steps of long division?
Divide, multiply, subtract, bring down. Ask how many times the divisor goes into the number you hold, write that digit above; multiply the divisor by it and write the product below; subtract; then bring the next digit of the dividend down beside the result. Repeat until the digits run out.
What do you do when the divisor is bigger than the first digit?
That column’s quotient digit is zero. Either write the 0 and continue, or take the first two digits of the dividend together and begin the answer one column to the right. For 952 ÷ 28 the 28 will not go into 9, so you start with 95 and the first digit of the answer sits above the 5.
How do you keep going after the remainder?
Put a decimal point in the quotient above the one in the dividend, then add zeros to the dividend and bring them down one at a time. Adding zeros after the point does not change the number’s value. For 8,536 ÷ 24 the remainder 16 becomes 160, and 24 goes into 160 six times with 16 left again.
How do you know when a long division will never end?
Watch the remainders. Every one is smaller than the divisor, so there are only finitely many. If a remainder you have already seen comes back, everything between the two sightings repeats forever. Dividing by 24, a returning remainder of 16 means the digit 6 repeats without end.
How do you do long division with a decimal?
Multiply both numbers by the same power of ten until neither has a decimal point, then divide as usual. The answer is unchanged. 15.6 ÷ 0.24 becomes 1,560 ÷ 24 = 65, and 0.84 ÷ 0.007 becomes 840 ÷ 7 = 120. Move both numbers, never just one.
How do you check a long division answer?
Multiply the divisor by the quotient and add the remainder. You should land exactly on the dividend. For 500 ÷ 32 = 15 remainder 20: 32 × 15 = 480, and 480 + 20 = 500. If that sum misses, a subtraction or a brought-down digit is wrong.
What is the longest a repeating decimal block can be?
One digit shorter than the divisor. Dividing by 7 there are only six possible non-zero remainders, so 1 ÷ 7 = 0.142857142857… repeats in a block of six. Dividing by 11 the block is shorter still: 245 ÷ 11 = 22.2727…, a block of two.
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