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Long Division Calculator

Enter a dividend and a divisor. You get the quotient and the remainder, the decimal answer to the places you choose, any repeating part and the working step by step.

Your numbers

Result

How we calculate it

Long division works through the dividend one digit at a time. Bring down the next digit to make a working number, find how many times the divisor fits into it (the quotient digit), multiply, and subtract to get the remainder. The remainder carries into the next step. Once the digits run out you can go on past the decimal point by adding a zero to the remainder.

For example, 125 ÷ 4 gives a quotient of 31 and a remainder of 1, and carrying on gives 31.25. 1000 ÷ 7 gives 142 remainder 6 and the decimal 142.857142…, where the digits 857142 repeat forever and are written 142.(857142).

Assumptions and limits

  • The decimal digits are cut off, not rounded. A dots mark (…) shows that the decimal goes on.
  • A fraction in lowest terms has a decimal that ends only when the denominator has no prime factors other than 2 and 5. Otherwise the decimal repeats.
  • Use whole numbers: a dividend up to 15 digits and a divisor up to 9 digits. The repeating pattern is searched for up to 5,000 digits.

Frequently asked questions

How do you do long division?

Take the digits of the dividend from the left. Divide the divisor into the working number, write the quotient digit, multiply and subtract, then bring down the next digit and repeat.

What is a remainder?

It is what is left over after dividing as many whole times as possible. 125 ÷ 4 is 31 with 1 left over, since 4 × 31 = 124.

Why do some decimals repeat?

When the remainder in the division repeats, the digits that follow repeat too. Since there are only as many possible remainders as the divisor, a repeat always appears sooner or later unless the remainder reaches zero.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Dividend (the number being divided) = 125; Divisor (the number you divide by) = 4; Decimal places to show = 6.

  • Quotient and remainder 31 remainder 1
  • Whole-number quotient 31
  • Remainder 1
  • Decimal quotient 31.25
  • Repeating pattern None (the decimal ends)

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.