Math
Long Division Calculator
Use this long division calculator to divide two whole numbers and see the work written out digit by digit, exactly the way it is set up in class: divide, multiply, subtract, bring down the next digit, and repeat.
Get the answer as a quotient with a remainder or as a decimal to your chosen number of places, and confirm it with the built-in check line (divisor × quotient + remainder = dividend). Negative numbers are handled with the standard sign rules.
The number being divided. It goes inside the long-division bracket.
The number you divide by. It goes outside the bracket and cannot be 0.
Try an example
Result
Answer
—
- Quotient (whole part)
- —
- Remainder
- —
- Decimal form
- —
- Check line
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the long division calculator solves
Use this long division calculator to divide two whole numbers and see the work written out digit by digit, exactly the way it is set up in class: divide, multiply, subtract, bring down the next digit, and repeat. Get the answer as a quotient with a remainder or as a decimal to your chosen number of places, and confirm it with the built-in check line (divisor × quotient + remainder = dividend). Negative numbers are handled with the standard sign rules.
Formula
How to use it
- Enter the dividend (the number being divided) and the divisor (the number you divide by).
- Choose Quotient + remainder for the classic whole-number answer, or Decimal answer to keep dividing past the decimal point.
- In decimal mode, pick how many decimal places to show (4 by default).
- Follow the steps digit by digit — each one shows the divide, multiply, subtract, and bring-down — then confirm the answer with the check line.
How to read the answer
The quotient tells you how many whole times the divisor fits into the dividend, and the remainder is what is left over — always smaller than the divisor. The check line, divisor × quotient + remainder = dividend, proves the answer is right. In decimal mode the remainder keeps generating digits: it either reaches 0 (the decimal terminates) or starts cycling (a repeating decimal, shown rounded at your chosen place). With negative numbers, the quotient is negative when the signs differ, and the remainder carries the dividend's sign.
Common mistakes and edge cases
- Forgetting to write a 0 in the quotient when the divisor does not go into the brought-down number — 612 ÷ 6 is 102, not 12.
- Letting a remainder equal or exceed the divisor at any step; when that happens, the quotient digit you wrote is too small.
- Misaligning place values when subtracting — keep each column lined up under the digit you brought down.
- Mixing sign conventions: here the remainder takes the dividend's sign (matching most calculators and C, Java, and JavaScript), while Python's % gives the remainder the divisor's sign instead.
- Expecting every decimal to end: quotients like 10 ÷ 3 repeat forever, so the decimal answer is rounded at the place you choose.
Worked examples
Classic division with a remainder
7,459 ÷ 6: 6 into 7 goes 1 (remainder 1), bring down 4 to make 14 (goes 2, remainder 2), bring down 5 to make 25 (goes 4, remainder 1), bring down 9 to make 19 (goes 3, remainder 1). Check: 6 × 1,243 + 1 = 7,459.
Answer
1,243 R 1
Decimal answer to four places
The same division continued past the decimal point by bringing down zeros, rounded at the fourth place.
Answer
1,243.1667
Dividend smaller than the divisor
8 does not go into 5, so the quotient is 0 and the whole dividend is the remainder. In decimal mode this becomes exactly 0.625.
Answer
0 R 5
Negative dividend
Divide the absolute values (7,459 ÷ 6 = 1,243 R 1), then apply the signs: the quotient is negative because the signs differ, and the remainder takes the dividend's negative sign. Check: 6 × (-1,243) + (-1) = -7,459.
Answer
-1,243 R -1
Repeating decimal
10 ÷ 3 produces remainder 1 forever, so the decimal digits repeat: 3.3333…
Answer
3.3333
Frequently asked questions
What does the R mean in a long division answer?+
R stands for remainder — the amount left over after the divisor has gone into the dividend as many whole times as possible. In 7,459 ÷ 6 = 1,243 R 1, the 6 fits 1,243 whole times and 1 is left over. The remainder is always smaller than the divisor.
What are the four steps of long division?+
Divide, Multiply, Subtract, Bring down — often remembered with the mnemonic "Does McDonald's Sell Burgers." You repeat the four steps once for each digit of the dividend, and each step block in this calculator shows one full cycle.
How do I turn the remainder into a fraction or a decimal?+
Put the remainder over the divisor for the fraction form: 1,243 R 1 with divisor 6 is 1,243 1/6. For the decimal form, keep dividing: write a decimal point and bring down zeros — that is exactly what this calculator's decimal mode does.
How does long division work with negative numbers?+
Divide the absolute values first, then apply the sign rules: the quotient is negative when the dividend and divisor have different signs. This calculator uses truncated division, so the remainder carries the dividend's sign — the convention used by most handheld calculators and by C, Java, and JavaScript.
Why does Python give a different quotient and remainder?+
Python's // and % use floored division, where the remainder takes the divisor's sign. For -7,459 ÷ 6, this calculator gives -1,243 R -1, while Python gives -7459 // 6 = -1244 and -7459 % 6 = 5. Both satisfy divisor × quotient + remainder = dividend; they just split it differently.
Why doesn't my decimal answer ever end?+
A division only terminates when the fraction dividend/divisor, fully reduced, has a denominator whose only prime factors are 2 and 5. Anything else — like 10 ÷ 3 or 1 ÷ 7 — produces a repeating decimal, which this calculator flags and rounds at your chosen number of places.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, or convert decimals to fractions with steps and visual fraction bars.
GCF and LCM Calculator
Find the greatest common factor and least common multiple for a list of positive integers with factor steps.
Prime Factorization Calculator
Factor a positive integer into primes and show the factor tree style division steps.
Ratio Calculator
Simplify ratios, compare two quantities, and find unit rates with clear proportional reasoning steps.
Binary Calculator
Add, subtract, multiply, or divide binary numbers with the column method shown: carries, borrows, partial products, and a long-division tableau, plus decimal, hex, and octal equivalents.
RREF Calculator
Reduce any matrix up to 8 x 8 to reduced row echelon form with every row operation shown, or enter A and b to solve Ax = b with unique, infinite (parametric), and no-solution reporting. Exact fractions throughout.
Last updated: May 8, 2026