Long Division Calculator

Quotient and remainder, explained by the long division calculator

Dividing one whole number by another rarely splits evenly. The quotient is how many whole times the divisor fits into the dividend, and the remainder is whatever is left over once the divisor cannot fit in again as a full amount. Together they describe the division exactly: multiplying the quotient by the divisor and adding the remainder always gives back the original dividend.

Take 17 divided by 5. The number 5 fits into 17 three whole times, since 5 times 3 is 15, and 15 is the closest multiple of 5 that does not go over 17. What is left over, 17 minus 15, is 2. So the quotient is 3 and the remainder is 2, and checking the arithmetic in reverse, 3 times 5 plus 2 comes back to 17.

A remainder is not a failure of the division, it is part of the answer: whole numbers do not always divide evenly, and the remainder captures how far off an even split the dividend actually is. When a dividend is smaller than the divisor, the quotient is simply 0 and the whole dividend becomes the remainder; dividing 5 by 17 gives a quotient of 0 and a remainder of 5.

The long-division method, step by step

Long division builds the quotient one digit at a time by working through the dividend's digits from left to right, rather than trying to divide the whole number at once. At each stage the process is the same four moves: bring down the next digit (or digits) of the dividend to form a partial dividend, work out how many times the divisor fits into that partial dividend, multiply the divisor by that count and subtract the result, and carry whatever is left over into the next step.

Working through 156 divided by 12, the same example the calculator above uses, illustrates every part of that process:

• Step 1. The first digit of 156 is 1, and 12 does not fit into 1 at all, so the next digit is brought down alongside it, forming 15. Now 12 fits into 15 exactly once (1 × 12 = 12), leaving a remainder of 15 − 12 = 3.
• Step 2. The next digit of 156, which is 6, is brought down and joined to the remainder carried from step 1, turning the 3 into 36. Now 12 fits into 36 exactly three times (3 × 12 = 36), leaving a remainder of 36 − 36 = 0.

Reading the quotient digits found at each step in order, 1 then 3, gives 13, and the final remainder is 0 because nothing was left over after the last step. So 156 divided by 12 is 13 with no remainder, which checks out: 13 × 12 = 156.

Every division this tool works through follows exactly that pattern, whether it needs one working step or several: bring down digits until there is enough to divide, record how many times the divisor fits, subtract, and carry the leftover into the next digit brought down. The table under the calculator's result shows that same working for whatever dividend and divisor you enter, row by row, so it can be checked against this explanation line by line.

A second worked example: exact division

Not every division needs more than one step to find every digit of the quotient, and not every division leaves a remainder behind. Take 100 divided by 4. The first digit of 100 is 1, and 4 does not fit into 1, so the second digit is brought down alongside it, forming 10. Now 4 fits into 10 exactly twice (2 × 4 = 8), leaving a remainder of 10 − 8 = 2. The third and final digit, 0, is brought down and joined to that remainder, turning the 2 into 20. Now 4 fits into 20 exactly five times (5 × 4 = 20), leaving a remainder of 20 − 20 = 0.

Reading the quotient digits in order, 2 then 5, gives 25, with a final remainder of 0. So 100 divided by 4 is exactly 25, and the check confirms it: 25 × 4 = 100. This is the case worth watching for, a remainder of 0 at the very last step means the division came out exact, with nothing left over.

More long division problems to practice on

A few more long division problems, worked the same digit-by-digit way, help make the four-move pattern, bring down a digit, divide, multiply, subtract, feel automatic before trying it with pencil and paper. Take 30 divided by 4: 4 does not go into 3, so the 0 is brought down to make 30, and 4 fits into 30 seven times (7 × 4 = 28), leaving a remainder of 2, so the answer is 7 remainder 2. Take 80 divided by 5 next: 5 fits into 8 once (1 × 5 = 5) with 3 left over, then the 0 is brought down to make 30, and 5 fits into 30 exactly six times (6 × 5 = 30) with nothing left over, so 80 divided by 5 comes out to a clean 16. Finally, 45 divided by 2: 2 fits into 4 twice (2 × 2 = 4) with none left over, then the 5 is brought down, and 2 fits into 5 twice (2 × 2 = 4) with 1 left over, giving a quotient of 22 remainder 1.

That is really the whole answer to how to divide any two whole numbers by hand: whatever the dividend and divisor, the steps above are how to do division from the first digit to the last, and the calculator at the top of the page runs through exactly this working for any numbers typed in, not just the long division problems worked through here.

Common mistakes to watch for

A few slip-ups account for most wrong answers in long division, and each is easy to avoid once named. Misaligning the digits is the most frequent, particularly when the quotient has a 0 in the middle (dividing 408 by 4 produces a 0 in the tens place, and skipping that 0 rather than writing it down shifts every later digit out of place). Forgetting to bring down a digit is the second most common error, usually showing up as a quotient with too few digits for the size of the dividend. The third is subtracting incorrectly when finding a step's remainder, which carries a wrong number into every step that follows even if the rest of the method is applied correctly.

The multiplication check described above (quotient × divisor + remainder = dividend) catches all three mistakes at once, which is why it is worth doing every time rather than only when an answer looks suspicious. It takes one multiplication and one addition, far less work than redoing the whole division.

Why the method still matters

Calculators and spreadsheets make the final quotient and remainder easy to get in an instant, but the long-division method itself is still worth understanding because the same digit-by-digit logic underlies converting a fraction to a decimal, checking whether one number divides evenly into another, and working with remainders in contexts like scheduling or splitting a quantity into equal groups. A calculator that only prints the final answer cannot show any of that; one that also shows the working, like the one above, lets you confirm each step matches what you would get by hand, and find exactly where a hand-worked answer went wrong if it does not match.

Other names for the same calculator

This page works as a long division calculator with steps, not just a division calculator that returns a bare quotient: every dividend and divisor you enter walks through the same long division method taught in school, digit by digit, which makes it a step by step division calculator, or a division calculator with steps, whenever the working matters as much as the final number. Because most real divisions do not split evenly, this also functions as a division calculator with remainder, a division with remainder calculator, a quotient and remainder calculator, or simply a remainder calculator or a remainder solver, depending on which number you actually need from a given problem.

If the original search was for long division with remainders, division with remainders more generally, or how to do long division from the very first step, this same page covers all three, and the digit-by-digit table below acts as a long division solver for any dividend and divisor, not only the worked examples above. The dividend divisor quotient remainder check at the end of each example, quotient times divisor plus remainder equals dividend, is exactly how to check long division answer by hand without redoing the whole long division method again. The same working also continues automatically into long division with decimals once a remainder appears, so long division steps done here double as long division practice, whether you need a division calculator online for a one-off answer or a long division of numbers tool to work through several problems in a row.