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Formula
dividend = divisor × quotient + remainder, with 0 ≤ remainder < divisor (for positive numbers)
- dividend
- the number being divided
- divisor
- the number you divide by (not 0)
- quotient
- how many whole times the divisor fits into the dividend
- remainder
- what is left over after taking away divisor × quotient
What the calculator shows
Enter a dividend and a divisor, and the long division calculator returns:
- The decimal quotient. Exact, with any repeating digits marked by a bar (0.16̅ for 1 ÷ 6).
- Quotient with remainder. The whole-number answer and what is left over, such as 378 R 1.
- Repeating decimal in parentheses. The same answer as 0.1(6), for places where a bar is hard to type, plus the repeating block and its length.
- Every step. Each divide, multiply, subtract and bring-down line, then a final check that divisor × quotient + remainder equals the dividend.
It accepts whole numbers, decimals and negative numbers, and it never rounds. Because it uses exact integer arithmetic, a problem such as 0.3 ÷ 0.1 gives exactly 3, not 2.9999999999999996.
How to do long division by hand
Long division breaks a big division into a series of small ones you can do in your head. Work through 5,293 ÷ 14:
- Divide. 14 does not go into 5, so take the first two digits: 52 ÷ 14 = 3. Write 3 above the 2.
- Multiply. 3 × 14 = 42.
- Subtract. 52 − 42 = 10.
- Bring down the next digit, 9, to make 109. 109 ÷ 14 = 7; 7 × 14 = 98; 109 − 98 = 11.
- Bring down 3 to make 113. 113 ÷ 14 = 8; 8 × 14 = 112; 113 − 112 = 1.
No digits are left, so 5,293 ÷ 14 = 378 R 1. Check it: 14 × 378 + 1 = 5,293.
Carrying on past the decimal point
To get the decimal, write a point after 378 and keep bringing down zeros. 10 ÷ 14 = 0 (remainder 10), 100 ÷ 14 = 7 (remainder 2), 20 ÷ 14 = 1 (remainder 6), then 4, 2, 8 and 5 follow, and the remainder 10 comes back. From there the digits 714285 repeat forever, so 5,293 ÷ 14 = 378.0(714285), written 378.07̅1̅4̅2̅8̅5̅ with a bar.
Long division with decimals
A decimal divisor is awkward to divide by, so move its decimal point until it is a whole number, and move the dividend’s point the same number of places. Multiplying both numbers by the same power of 10 leaves the quotient unchanged.
For 4.35 ÷ 0.6, the long division calculator moves both points two places (the larger of the two decimal lengths) to get 435 ÷ 60 = 7 R 15, then 150 ÷ 60 = 2 R 30 and 300 ÷ 60 = 5 R 0. The answer is 7.25. By hand you would usually move just one place to get 43.5 ÷ 6; both routes give the same quotient. The remainder in the original units is 0.15, because 0.6 × 7 + 0.15 = 4.35.
Decimal values of common fractions
Dividing 1 by a whole number gives the decimal of a unit fraction. Values below were produced by the calculator.
| Division | Decimal | Type |
|---|---|---|
| 1 ÷ 2 | 0.5 | terminating |
| 1 ÷ 3 | 0.(3) | repeating, 1 digit |
| 1 ÷ 4 | 0.25 | terminating |
| 1 ÷ 6 | 0.1(6) | repeating after 1 digit |
| 1 ÷ 7 | 0.(142857) | repeating, 6 digits |
| 1 ÷ 8 | 0.125 | terminating |
| 1 ÷ 9 | 0.(1) | repeating, 1 digit |
| 1 ÷ 11 | 0.(09) | repeating, 2 digits |
| 1 ÷ 12 | 0.08(3) | repeating after 2 digits |
| 1 ÷ 13 | 0.(076923) | repeating, 6 digits |
| 1 ÷ 15 | 0.0(6) | repeating after 1 digit |
| 1 ÷ 16 | 0.0625 | terminating |
The pattern follows from the divisor’s prime factors. Only 2s and 5s (as in 2, 4, 8, 16) give a decimal that ends. Any other prime factor, such as the 3 in 6, 12 and 15, makes it repeat. To turn other fractions into decimals or simplify them, the fraction calculator and the decimal calculator work the other way around.
Long division with negative numbers
Divide the absolute values, then fix the sign (the long division calculator does the same): the quotient is negative when exactly one of the two numbers is negative. So −29 ÷ 4 = −7.25 and 29 ÷ −4 = −7.25. For the whole-number form, the calculator truncates toward zero and gives the remainder the dividend’s sign: −29 ÷ 4 = −7 R −1, because 4 × (−7) + (−1) = −29. Some textbooks prefer a remainder that is never negative (−8 R 3); both satisfy dividend = divisor × quotient + remainder.
Where long division is used
- Sharing and grouping. 5,293 chairs in rows of 14 make 378 full rows with 1 chair left over.
- Unit rates and prices. Dividing a total cost by a quantity gives the price per item.
- Checking factors. A remainder of 0 shows the divisor is a factor, which helps when finding a greatest common factor.
- Converting fractions. Every fraction is a division, and long division gives its exact decimal.
Common mistakes
- Forgetting a zero in the quotient. When the divisor does not go into the current number, write 0 before bringing down the next digit (as in 378.07…).
- A remainder bigger than the divisor. That means the quotient digit was too small; increase it by one.
- Moving only one decimal point. Shift the dividend’s point by the same number of places as the divisor’s.
- Stopping a repeating decimal too early. Watch for a remainder you have seen before instead of rounding.
Glossary
- Dividend. The number being divided.
- Divisor. The number you divide by.
- Quotient. The result of the division.
- Remainder. What is left after the divisor has been taken out as many whole times as possible.
- Repeating decimal. A decimal whose digits eventually repeat in a fixed block forever, also called a recurring decimal.
Worked examples
Four-digit dividend with a remainder
Divide 8,746 by 25: the quotient is 349 R 21, and the decimal 349.84 terminates.
Inputs: Dividend (number being divided) = 8746; Divisor (number you divide by) = 25
87 (the first 2 digits): 87 ÷ 25 = 3; 3 × 25 = 75; 87 − 75 = 12 Bring down 4 → 124: 124 ÷ 25 = 4; 4 × 25 = 100; 124 − 100 = 24 Bring down 6 → 246: 246 ÷ 25 = 9; 9 × 25 = 225; 246 − 225 = 21 Write the decimal point and bring down 0 → 210: 210 ÷ 25 = 8; 8 × 25 = 200; 210 − 200 = 10 Bring down 0 → 100: 100 ÷ 25 = 4; 4 × 25 = 100; 100 − 100 = 0 Remainder 0: the decimal terminates. Check: 8,746 = 25 × 349 + 21
Answer: 8,746 ÷ 25 = 349.84 (quotient 349 R 21)
A repeating decimal
47 ÷ 12 gives 3 R 11; carrying on past the decimal point, the 6 repeats forever.
Inputs: Dividend (number being divided) = 47; Divisor (number you divide by) = 12
47 (the first 2 digits): 47 ÷ 12 = 3; 3 × 12 = 36; 47 − 36 = 11 Write the decimal point and bring down 0 → 110: 110 ÷ 12 = 9; 9 × 12 = 108; 110 − 108 = 2 Bring down 0 → 20: 20 ÷ 12 = 1; 1 × 12 = 12; 20 − 12 = 8 Bring down 0 → 80: 80 ÷ 12 = 6; 6 × 12 = 72; 80 − 72 = 8 Remainder 8 has appeared before, so the digit 6 repeats forever. Check: 47 = 12 × 3 + 11
Answer: 47 ÷ 12 = 3.91(6) (quotient 3 R 11)
Decimal divisor
Move the decimal point two places in both numbers, so 9.6 ÷ 0.32 becomes 960 ÷ 32.
Inputs: Dividend (number being divided) = 9.6; Divisor (number you divide by) = 0.32
Move the decimal point 2 places right in both numbers: 9.6 ÷ 0.32 = 960 ÷ 32 96 (the first 2 digits): 96 ÷ 32 = 3; 3 × 32 = 96; 96 − 96 = 0 Bring down 0 → 0: 0 ÷ 32 = 0; 0 × 32 = 0; 0 − 0 = 0 Remainder 0: the division is exact. Check: 9.6 = 0.32 × 30 + 0
Answer: 9.6 ÷ 0.32 = 30
Negative dividend smaller than the divisor
Edge case: −5 ÷ 7, where the divisor does not go into the dividend and the answer is a six-digit repeating cycle.
Inputs: Dividend (number being divided) = -5; Divisor (number you divide by) = 7
Divide the absolute values, then give the answer a minus sign (the signs differ). 5 (the first digit): 5 ÷ 7 = 0; 0 × 7 = 0; 5 − 0 = 5 Write the decimal point and bring down 0 → 50: 50 ÷ 7 = 7; 7 × 7 = 49; 50 − 49 = 1 Bring down 0 → 10: 10 ÷ 7 = 1; 1 × 7 = 7; 10 − 7 = 3 Bring down 0 → 30: 30 ÷ 7 = 4; 4 × 7 = 28; 30 − 28 = 2 Bring down 0 → 20: 20 ÷ 7 = 2; 2 × 7 = 14; 20 − 14 = 6 Bring down 0 → 60: 60 ÷ 7 = 8; 8 × 7 = 56; 60 − 56 = 4 Bring down 0 → 40: 40 ÷ 7 = 5; 5 × 7 = 35; 40 − 35 = 5 Remainder 5 has appeared before, so the digits 714285 repeat forever. Check: −5 = 7 × 0 + (−5)
Answer: −5 ÷ 7 = −0.(714285) (quotient 0 R −5)
Assumptions and limitations
- Dividend from −1,000,000,000,000,000 to 1,000,000,000,000,000 and divisor from −1,000,000,000,000 to 1,000,000,000,000, each with up to 8 decimal places. The divisor cannot be 0.
- All arithmetic uses exact whole-number (big-integer) math, so results have no rounding errors. Decimals are handled by moving the decimal point in both numbers by the same number of places, which does not change the quotient.
- The decimal quotient continues until the remainder is 0 (a terminating decimal) or a remainder repeats (a repeating decimal). Repeating digits are shown with a bar over them and in parentheses, as in 0.1(6) for 1 ÷ 6.
- Up to 200 decimal places are searched for a repeating cycle. Cycles longer than 30 digits are abbreviated with "…" in the main result, and the working lists the first 12 steps after the decimal point.
- With negative numbers the quotient is truncated toward zero and the remainder takes the sign of the dividend, so −17 ÷ 5 = −3 R −2 because −17 = 5 × (−3) + (−2).
- With decimal inputs, the remainder is given in the original units, so 7.5 ÷ 0.4 = 18 R 0.3 because 0.4 × 18 + 0.3 = 7.5.
Frequently asked questions
How do you do long division step by step?
Repeat four steps: divide, multiply, subtract, bring down. Divide the first part of the dividend by the divisor and write the whole-number answer on top. Multiply that digit by the divisor, subtract the product, then bring down the next digit and repeat until no digits are left. What remains is the remainder.
How do you do long division with decimals?
Move the decimal point in the divisor to the right until it is a whole number, and move the dividend's point the same number of places, adding zeros if needed. Then divide as usual and put the decimal point in the answer directly above the dividend's point. For 2.88 ÷ 0.4, divide 28.8 by 4 to get 7.2.
How do I turn the remainder into a decimal?
Instead of stopping at the remainder, write a decimal point after the quotient, add a 0 to the remainder and keep dividing. 9 ÷ 4 is 2 R 1; bringing down a 0 gives 10 ÷ 4 = 2 R 2, then 20 ÷ 4 = 5 R 0, so 9 ÷ 4 = 2.25.
How do you know if a decimal repeats?
Watch the remainders. There are only as many possible remainders as the divisor's size, so if the decimal does not end, a remainder must eventually come back. As soon as one does, the digits since its first appearance repeat forever. A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5.
What if the dividend is smaller than the divisor?
The whole-number quotient is 0 and the remainder is the dividend itself, so 5 ÷ 8 = 0 R 5. Write 0 and a decimal point, bring down a 0 and continue to get the decimal, here 0.625.
Why can't you divide by zero?
Division asks what number times the divisor gives the dividend. No number times 0 gives a nonzero dividend, and every number times 0 gives 0, so there is no single answer. Division by zero is undefined, and the calculator asks for a different divisor.
How do you check a long division answer?
Multiply the quotient by the divisor and add the remainder; you should get the dividend back. For 5,293 ÷ 14 = 378 R 1, 14 × 378 = 5,292, and 5,292 + 1 = 5,293. The calculator shows this check as its last step.
Sources
- Long Division — Wolfram MathWorld. Checked October 10, 2026.
- Repeating Decimal — Wolfram MathWorld. Checked October 10, 2026.
- Remainder — Wolfram MathWorld. Checked October 10, 2026.