About Long Division Calculator
This long division calculator is free, needs no sign-up and runs in your browser, so the numbers you type are never uploaded. It draws the working in the bracket layout you know from school: the quotient on top, the divisor in front of the bracket, and below the dividend each product, the line under it and the remainder with the next digit brought down.
It has three modes. With remainder gives a whole-number quotient and a remainder, as in 4325 ÷ 12 = 360 remainder 5. With decimals keeps dividing past the decimal point, stops when the answer ends, and detects repeating decimals: 22 ÷ 7 = 3.(142857) with the repeating block marked by a bar. Polynomials divides one polynomial by another in the same layout.
Decimal inputs are allowed. When the divisor has decimals, both numbers are shifted the same number of places so the divisor becomes a whole number, and the calculator tells you how far it moved. The layout sits inside its own scroll area, so it stays readable on a phone.
How to use Long Division Calculator
- Choose With remainder, With decimals or Polynomials.
- Type the dividend (the number being divided) and the divisor (the number you divide by).
- In decimal mode, choose how many decimal places you want at most.
- Read the quotient and remainder at the top, then follow the drawn layout below.
- Open the steps to see each digit: divide, multiply, subtract, bring down. The check line multiplies back to confirm.
Features
- The classic bracket layout, drawn with real columns and lines.
- Quotient and remainder for whole numbers, with the mixed-number form.
- Decimal expansion that stops when it ends or repeats, with the repeating block marked.
- Decimal dividends and divisors, with the decimal point shifted for you.
- Polynomial long division with exact fractions and the quotient plus remainder form.
- Step-by-step list and a multiplication check.
- Negative numbers and rounded results for long periods.
The division algorithm
Long division repeats four moves for each digit: divide, multiply, subtract, bring down the next digit. It produces a quotient q and a remainder r that satisfy the relationship below, with r always smaller than the divisor.
A decimal expansion repeats exactly when a remainder comes up for a second time, because the digits that follow then repeat too. There are at most (divisor - 1) different remainders, so the repeating block is never longer than that.
dividend = divisor × quotient + remainder
0 ≤ remainder < divisor
repeat length ≤ divisor - 1Worked examples
4325 ÷ 12 gives 360 remainder 5
Check: 12 × 360 + 5 = 4325.
7845 ÷ 8 gives 980.625
The remainder reaches zero after three decimal places, so the decimal ends.
22 ÷ 7 gives 3.(142857)
The remainder 1 comes up again after six digits, so 142857 repeats forever.
(2x³ + 3x² - 5x + 6) ÷ (x + 3) gives 2x^2 - 3x + 4 remainder -6
Polynomial long division: divide the leading terms, multiply back, subtract and bring down.
Good to know
Limits
Decimal mode shows at most 30 places. If a long period does not close inside the places you chose, the digits are cut off, and a correctly rounded value is shown next to them.
Polynomial mode divides polynomials in one variable with rational coefficients. Expand any brackets first.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- If the remainder is not zero when the digits run out, either write it as a remainder or put a decimal point and keep adding zeros.
- A decimal ends only if the divisor, in lowest terms, has no prime factors other than 2 and 5.
- To check any answer, multiply the quotient by the divisor and add the remainder. You should get the dividend.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How does long division work?
For each digit of the dividend you divide to find a quotient digit, multiply it back by the divisor, subtract to get a remainder and bring down the next digit. You repeat until the digits run out.
How do I do long division with decimals?
If the divisor has decimals, move the decimal point of both numbers the same number of places until the divisor is whole. Then divide as usual, adding zeros after the point as needed.
How can I tell a decimal repeats?
When a remainder you have already had comes up again, the same digits will follow. The calculator marks the repeating block with a bar, as in 0.1(6) for 1/6.
What is the remainder?
It is what is left over when the divisor no longer fits. It is always smaller than the divisor, and zero means the division is exact.
Can it divide polynomials?
Yes. Choose Polynomials and enter, for example, 2x^3+3x^2-5x+6 divided by x+3. The result is a quotient and a remainder.
Why is the division by zero refused?
No number multiplied by zero gives a non-zero dividend, so there is no answer. The calculator says so instead of looping.
Popular Long Division Calculator pages
- Long Division With RemaindersEnter two whole numbers to get the quotient and remainder, with the layout drawn out.
- Long Division With DecimalsDivide decimals or carry the division on past the point, with every step drawn.
- Polynomial Long Division CalculatorEnter two polynomials to divide, with the layout drawn out term by term.
- Repeating Decimal CalculatorDivide two numbers and see the repeating block marked, such as 1 ÷ 7 = 0.(142857).