Long Division Calculator
Divide two whole numbers to see the quotient, remainder and decimal expansion.
What this tool does
Long division finds how many times the divisor goes into the dividend and what is left. 22 ÷ 7 is 3 remainder 1, and continuing the division gives the decimal 3.142857142857…, in which the digits 142857 repeat. Enter any whole numbers above.
Calculates the whole-number quotient and the remainder.
Continues the division to produce the decimal, detecting a repeating cycle.
How to use it
- Enter the dividend.
- Enter the divisor.
- Read the quotient and remainder.
- Read the decimal form and whether it repeats.
Why use this calculator
Gives the quotient and remainder of a whole-number division and the full decimal expansion, with the repeating digits shown in brackets. Division by hand produces remainders and repeating decimals that are easy to get wrong. The calculator shows both, and the repeating cycle length is a useful check for fractions and number theory.
Why we built it
We built the long division calculator to give the quotient, remainder and decimal expansion, with the repeating cycle marked in brackets. Turn the answer into a fraction with the decimal to fraction calculator, or work with fractions on the fraction calculator.
Who this tool is for
- Students learning long division
- Parents helping with homework
- Anyone looking for repeating decimals
When to use it
- Checking homework.
- Converting fractions to decimals.
- Finding a repeating pattern.
- Splitting items into groups with a remainder.
How it works
Divide the dividend by the divisor to get the whole-number quotient, and keep the remainder. For the decimal part, multiply the remainder by 10, divide again, and repeat. If a remainder repeats, the digits between its two appearances repeat forever.
Example: 22 ÷ 7. Quotient 3 remainder 1. Then 10÷7 = 1 r 3, 30÷7 = 4 r 2, 20÷7 = 2 r 6, 60÷7 = 8 r 4, 40÷7 = 5 r 5, 50÷7 = 7 r 1. The remainder 1 returns, so the cycle 142857 repeats.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Dividend | 22 |
| Divisor | 7 |
With those inputs, the calculator returns:
- Quotient and remainder: 3 remainder 1
- Decimal form: 3.(142857) (digits in brackets repeat)
- Repeating cycle length: 6 digits
- Check: 3 × 7 + 1 = 22
What you give it, and what you get back
| Item | Details |
|---|---|
| Dividend and divisor | Whole numbers; the divisor must be above zero. |
| Output | Quotient, remainder, decimal form, repeat cycle length and a check. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Divisor error | Division by zero is undefined. | Enter a divisor above zero. |
| Decimals entered | Only whole numbers are supported. | Multiply both by a power of ten to remove decimals. |
| Decimal is long | The repeating cycle can be long. | Shown in full up to the cycle or 40 digits. |
Assumptions and limitations
- Whole numbers only.
- Decimals are shown up to 40 digits.
Frequently asked questions
How do I do long division?
Divide, multiply, subtract and bring down the next digit, repeating until done.
What is a remainder?
What is left over when the divisor does not divide the dividend exactly.
What is a repeating decimal?
A decimal whose digits repeat forever, like 1/3 = 0.333….
How do I know if a fraction terminates?
It terminates only if the denominator in lowest terms has no prime factors other than 2 and 5.
Can it divide decimals?
No, only whole numbers.
Is my data sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.
Sources and accuracy
Results follow the standard division algorithm, in which the dividend equals divisor times quotient plus remainder, together with the exact decimal expansion of the quotient.
Figures last checked against the source on . Standards and rates can change — if you are relying on this for something that matters, confirm against the source above. Think a figure is wrong or out of date? Send a correction.