Long Division Calculator
Quotient, remainder and the written working, one digit at a time.
Updated
The number being divided.
The number you are dividing by.
Quotient and remainder
22 r 2
1,234 ÷ 56
- Quotient
- 22
- Remainder
- 2
- As a decimal
- 22.035714
- Check
- 22 × 56 + 2 = 1,234
The working, one digit at a time
| Bring down | Goes in | Subtract | Left |
|---|---|---|---|
| 1 | 0 | 0 | 1 |
| 12 | 0 | 0 | 12 |
| 123 | 2 | 112 | 11 |
| 114 | 2 | 112 | 2 |
The check line is the definition of division rather than a nicety: quotient times divisor plus remainder must return the dividend exactly. If it does not, the working went wrong somewhere above.
In short
What is 1234 divided by 56?
22 remainder 2, or 22.0357 as a decimal. The check is that 22 × 56 + 2 returns 1234 exactly. Long division reaches it one digit at a time: 12 holds no 56s, 123 holds two, and the 14 left over holds none.
Quotient times divisor plus remainder must equal the dividend. That is the definition, and it is the only check you need.
How to use the long division calculator
Long division breaks one large division into a sequence of small ones. Instead of asking how many 56s fit into 1234 all at once, it asks the question digit by digit, carrying whatever is left over into the next step. The method is old, mechanical and entirely reliable, which is why it survives in classrooms long after calculators made the answer trivial to get.
The four names are worth fixing early because every explanation uses them. The dividend is the number being divided. The divisor is what you divide by. The quotient is the answer, and the remainder is whatever is left over that the divisor could not take. Together they satisfy one equation, and that equation is both the definition of division and the way to check any answer.
22 r 2
1234 divided by 56
quotient and remainder
22.0357
The same, as a decimal
the remainder continued
1234
22 × 56 + 2
the check that closes it
The remainder and the decimal are the same information in two forms. Two left over out of 56 is 2/56 of another whole one, which is 0.0357 — so 22 remainder 2 and 22.0357 describe an identical result. Which you want depends on the question: remainders suit counting problems, decimals suit measurement.
The working itself is where the value is. Each row of the table shows the number currently being divided, how many times the divisor goes into it, what that multiplies out to, and what is left after subtracting. That sequence is the part somebody checking a child's homework, or their own, actually needs — the final answer alone tells you nothing about where it went wrong.
- Dividend
- the number being divided
- Divisor
- the number you divide by
- Quotient
- how many times it goes in
- Remainder
- what is left over
- The identity
- quotient × divisor + remainder = dividend
The remainder is always smaller in magnitude than the divisor. If it is not, the quotient was too small and another whole divisor could still have been taken out.
When the remainder should be a fraction
A remainder over the divisor is a fraction, and that fraction often wants reducing before it is useful. That page does the arithmetic exactly.
Open the fraction calculator →Divisions worked out both ways, with the check shown so each row can be confirmed rather than trusted.
| Division | Quotient and remainder | Decimal |
|---|---|---|
| 7 ÷ 2 | 3 r 1 | 3.5 |
| 144 ÷ 12 | 12 r 0 | 12 |
| 1234 ÷ 56 | 22 r 2 | 22.0357 |
| 100 ÷ 7 | 14 r 2 | 14.2857 |
| 500 ÷ 25 | 20 r 0 | 20 |
| 365 ÷ 7 | 52 r 1 | 52.1429 |
| 1000 ÷ 3 | 333 r 1 | 333.3333 |
| 847 ÷ 11 | 77 r 0 | 77 |
| 2024 ÷ 8 | 253 r 0 | 253 |
| 999 ÷ 37 | 27 r 0 | 27 |
| −17 ÷ 5 | −3 r −2 | −3.4 |
The method, one digit at a time
Work left to right through the dividend. Bring down the next digit, ask how many times the divisor fits into what you now have, write that above, multiply it back, subtract, and carry the difference into the next step. The process ends when the digits run out, and whatever is left at that point is the remainder.
- Bring down 1
- 56 goes in 0 times, 1 left
- Bring down 2 → 12
- 0 times, 12 left
- Bring down 3 → 123
- 2 times, 112, leaves 11
- Bring down 4 → 114
- 2 times, 112, leaves 2
- Answer
- 22 remainder 2
The leading zeros are real steps and are usually not written down, which is why the quotient is 22 rather than 0022. Every digit of the dividend gets a row whether or not it contributes to the answer.
Carrying on past the decimal point works the same way: add a zero, bring it down, and keep going. Two becomes twenty, 56 goes into it zero times; twenty becomes two hundred, 56 goes in three times leaving 32, and so on. The remainder never disappears, it just moves further down the decimal places.
Negative numbers, where the conventions split
Dividing a negative number raises a question that ordinary arithmetic does not: what sign should the remainder take? Two answers are in use, both internally consistent, and they disagree about the same calculation. This matters because one of them is what programming languages do and the other is what number theory requires.
Do
- Check every answer with quotient × divisor + remainder
- Expect the remainder to be smaller than the divisor
- Continue past the decimal point by bringing down zeros
- State which convention you are using for negative dividends
Don't
- Divide by zero — no quotient exists that could reconstruct the dividend
- Assume a calculator remainder matches the Division Algorithm
- Drop the rows where the divisor goes in zero times
- Treat the remainder as a decimal without dividing it by the divisor first
For −17 divided by 5, truncating division gives a quotient of −3 and a remainder of −2, which is what this page and most programming languages produce. The Division Algorithm in number theory instead requires the remainder to be non-negative, giving a quotient of −4 and a remainder of 3. Both satisfy the check equation, so neither is arithmetically wrong — but quoting one where the other was expected is.
The formula, worked line by line
One identity, and everything else in the method is bookkeeping around it. That identity is what makes a remainder meaningful rather than merely something left over at the end.
“Quotient times divisor plus remainder equals the dividend. Everything long division does is find the largest quotient that keeps the remainder smaller than the divisor.”
Read that way, the whole method has one goal: take out as many whole divisors as possible. The digit-by-digit procedure is simply an efficient way of doing that without having to guess.
dividend = quotient × divisor + remainder
remainder < |divisor|, always
decimal = quotient + remainder ÷ divisor
remainder as a fraction = remainder / divisor
nothing divides by zero- 100 ÷ 7
- 14 remainder 2
- The remainder as a fraction
- 2/7
- As a decimal
- 0.285714…
- Added to the quotient
- 14.285714…
- Both forms
- 14 r 2 and 14.2857
Sevenths repeat with a six-digit cycle — 142857 — which recurs forever in some order for every seventh. That is a property of the denominator rather than of the division: a decimal terminates only when the reduced denominator has no prime factors other than 2 and 5.
Why nothing divides by zero
The check equation explains it better than any rule. Dividing 10 by 0 would need a quotient q with q × 0 + r = 10, and q × 0 is zero whatever q is. No value works, so the operation has no answer — not infinity, which is not a number that could satisfy the equation either.
Whether it is still taught
- US Common Core
- fluency with the standard algorithm by grade 6
- The standard code
- 6.NS.B.2
- What "standard algorithm" means
- is not spelled out in the wording
- Classroom practice
- varies by state and by scheme
- The check
- is taught everywhere, under every method
Adoption and interpretation differ, so the honest statement is that fluency with a standard algorithm for multi-digit division is required by grade 6 rather than that long division specifically is mandated everywhere.
Whichever method a school uses, the reason for teaching one at all is the same: a procedure you can follow and check is worth more than an answer you cannot verify, particularly when the answer came from a device that will not show its working.
Questions people ask
Sources
Where the constants and formulas on this page come from. Each line names the figure it backs.
For integers a and b with b non-zero, there exist a quotient and remainder satisfying a = bq + r, and the remainder is constrained in magnitude by the divisor.
Division Algorithm — Wolfram MathWorld
Students fluently divide multi-digit numbers using the standard algorithm by grade six.
CCSS.Math.Content.6.NS.B.2 — Common Core State Standards Initiative
Division by zero is undefined, because no quotient satisfies the defining equation.
Division by Zero — Wolfram MathWorld
Related guides
How Are Loan Payments Calculated? Amortization, Explained
One level payment, front-loaded interest — the formula worked by hand, the two levers you control, and why the smaller payment is often the costlier loan.
July 23, 2026 · 13 min read
How Does Inflation Work? The Math That Shrinks Money
One growth factor, two answers — what today's money will buy later, and how many future dollars it takes to keep up.
July 23, 2026 · 13 min read
How Is Sales Tax Calculated? Rates, Rules, and the Reverse Math
The combined-rate reality, the one-multiplication forward formula, and the division that pulls the tax back out of any total.
July 23, 2026 · 13 min read