How to use the long division calculator
- Enter the dividend (the number being divided) and the divisor (the number you divide by). Both must be whole numbers, and the divisor cannot be zero.
- Choose whether you want the answer as a quotient and remainder or as a decimal, and for decimals pick how many places to show.
- Read the quotient, remainder, mixed number and exact decimal. A repeating decimal is written with parentheses around the repeating block.
- Follow the step table: each row brings down a digit, divides, multiplies and subtracts to find the new remainder.
Formula
dividend = quotient x divisor + remainder, with 0 <= remainder < divisor
At each step: number = previous remainder x 10 + next digit
Quotient digit = whole number of times the divisor fits into that number
New remainder = number - quotient digit x divisor
To continue into decimals, bring down zeros after the decimal point and repeat the same steps. If a remainder appears twice, the digits between its two appearances repeat forever. All arithmetic uses exact whole numbers, so there is no rounding until the final decimal is shown.
Worked example
Divide 1,234 by 7. The first digit 1 is smaller than 7, so the quotient digit is 0 and the remainder is 1. Bring down 2 to make 12: 7 goes into 12 once, 1 x 7 = 7, and 12 - 7 leaves 5.
Continuing gives a quotient of 176 and a remainder of 2, because 7 x 176 + 2 = 1,234. As a mixed number that is 176 2/7.
Carrying on with zeros gives the exact decimal 176.(285714), where 285714 repeats. Other cases: 1/8 ends at 0.125, 1/3 is 0.(3), 1/6 is 0.1(6), 1/7 repeats every 6 digits, and 2/3 rounds to 0.6667 at 4 places.
How long division works
Long division breaks a big division into a series of small ones, one digit at a time. You look at the leftmost digits of the dividend until they form a number at least as big as the divisor, find how many times the divisor fits, write that digit above, subtract the product, and bring down the next digit. The step table in this tool shows each of those moves so you can check homework or learn the method.
Remainders and decimals
A remainder is what is left over when the divisor no longer fits. If you keep going into decimals, the process either stops (when a remainder is 0) or repeats (when a remainder you have seen before returns). A fraction in lowest terms ends exactly when its denominator has only the prime factors 2 and 5, which you can check with the prime number calculator. To go the other way and turn a decimal into a fraction, see fraction to decimal.
Limits
The tool keeps results readable and safe.
- Dividend and divisor must be whole numbers from 0 and 1 up to 10^15.
- Decimal places run from 0 to 50, and the step table shows the first 60 steps.
- If a repeating block is longer than 20,000 digits, only the start of the decimal is shown and the page says so.
Assumptions and limits
- Only whole-number dividends and divisors are accepted. Negative numbers and decimals are rejected with a message.
- Rounded decimals use half-up rounding on exact digits, so 1/8 to 2 places is 0.13.
- Repeating decimals are written with parentheses around the block that repeats.
- The step table follows the standard school method. Some countries draw the layout differently, but the arithmetic is identical.
- Everything runs in your browser. Nothing you enter is sent anywhere.
Frequently asked questions
How do you do long division with a remainder?
Work through the digits one at a time, dividing, multiplying and subtracting. What is left at the end is the remainder. For 1,234 divided by 7 the quotient is 176 and the remainder is 2.
How do I know if a decimal repeats?
If a remainder shows up a second time while you continue into decimals, the digits repeat from that point. The calculator marks the repeating block with parentheses and tells you its length.
What does the quotient digit zero mean in the first step?
It means the first digits of the dividend are still smaller than the divisor, so the divisor fits zero times. The calculator keeps the row so you can see the method, even though leading zeros are not written in the final quotient.
Can I divide by a decimal or a negative number?
Not here. This tool teaches whole-number long division. To divide decimals, multiply both numbers by the same power of 10 until the divisor is whole, then enter the results.
Why does the mixed number differ from the decimal?
They are two forms of the same value. The mixed number is the quotient plus the remainder over the divisor, such as 176 2/7, and the decimal is the same amount written with digits, 176.285714 and so on.