What long division does
Long division is the pencil-and-paper method for dividing one number (the dividend) by another (the divisor) one digit at a time. It produces a quotient and, when the numbers do not divide evenly, a remainder. This calculator shows the schoolbook layout and a plain sentence for every step, so you can check homework, see where you made a slip or learn the method. It handles whole numbers with a remainder and decimal numbers with a terminating or repeating quotient, using exact whole-number arithmetic.
Divide, multiply, subtract, bring down
Every long division is the same four moves repeated: divide the current number by the divisor to get the next digit of the quotient, multiply that digit by the divisor, subtract the product to get a remainder and bring down the next digit. For 100 ÷ 7 the first two steps read: 7 does not go into the first digit, so take the first 2 digits: 10. 7 goes into 10 1 time (7 × 1 = 7). Subtract: 10 − 7 = 3. Bring down the 0: 30. 7 goes into 30 4 times (7 × 4 = 28). Subtract: 30 − 28 = 2. The dividend has no digits left, so the whole-number part of the quotient is 14 and the remainder is 2. The remainder is always smaller than the divisor; if it were not, the divisor would fit in again.
Quotient and remainder
In whole-number mode the answer is written as a quotient and a remainder: 100 ÷ 7 = 14 remainder 2. You can check any such answer with the identity dividend = divisor × quotient + remainder, which here is 100 = 7 × 14 + 2. This mode is for a nonnegative whole-number dividend and a positive whole-number divisor, the way division with remainders is taught first. For negative or decimal numbers use the decimal mode.
Continuing into decimals
To get a decimal answer, put a decimal point in the quotient and keep going by bringing down zeros. For 1 ÷ 8 the first step cannot divide 1 by 8, so the whole part is 0, and the zeros give 10, 20 and 40 divided by 8 in turn. The remainder reaches 0 after three digits and the quotient is 0.125. A division whose remainder reaches 0 gives a terminating decimal. The calculator labels this outcome so you know the answer is exact, not cut off.
Repeating decimals
Some divisions never reach a zero remainder. For 100 ÷ 7 the remainders after the decimal point are 2, 6, 4, 5, 1, 3 and then 2 again. Because the same remainder appears twice, the digits must repeat from that point on: the quotient is 14.(285714), where the digits in brackets, 285714, repeat forever. The block has 6 digits. The same thing happens with 1 ÷ 6, which is 0.1(6): here one digit, 1, comes before the repeating 6.
There is a limit on how long a repeating block can be. Each remainder is a whole number smaller than the divisor, so after at most (divisor − 1) steps a remainder must repeat. For 1 ÷ 97 the block can be up to 96 digits long, which is longer than the 20 decimal places this calculator can show, so the result is labelled as truncated: the calculator shows 20 digits and says that no repeating block has appeared yet. A fraction in lowest terms has a terminating decimal exactly when its denominator has no prime factors other than 2 and 5. To reduce a fraction to lowest terms first, use the GCF calculator.
Dividing by a decimal
To divide by a decimal, multiply the divisor and the dividend by the same power of ten until the divisor is a whole number. Multiplying both by the same number does not change the quotient, because it scales the top and the bottom of the fraction equally. For 12.6 ÷ 0.3 both numbers are multiplied by 10, giving 126 ÷ 3, and the quotient is 42. The calculator prints this scaling step when it is needed, and the steps and layout then use the whole numbers. Trailing zeros do not matter: 10.50 ÷ 0.5 is 21.
Negative numbers, truncating and rounding
The sign of the quotient is positive when the dividend and divisor have the same sign and negative when they differ, so -7 ÷ 4 is -1.75. The long division itself is done on the sizes of the numbers and the sign is added at the end. The decimal places you choose, from 1 to 20, control how far the division continues. The digits are truncated, not rounded: 22 ÷ 7 stopped after 3 places is 3.142, whereas rounding to 3 places would give 3.143 because the next digit is 8. The calculator says "truncated" whenever it stops before the remainder reaches 0 or a block repeats.
Limits and what the page shows
Each number can have up to 12 digits and up to 6 decimal places, and the divisor cannot be zero. To keep the page readable, the layout and the written steps show at most the first 16 steps; if the division needs more, the page says how many there are and the digits of the quotient above are still complete. For very large or very small values, convert them with the scientific notation calculator, and to compare a calculated value with a measured one use the percent error calculator.
Long division questions
How do I do long division with a remainder?
Divide, multiply, subtract and bring down until no digits are left. What remains is the remainder. For 100 ÷ 7 the quotient is 14 and the remainder is 2.
How do I know when a decimal quotient repeats?
When a remainder appears that you have seen before, the digits that follow will repeat. The calculator watches for this and marks the block in brackets, for example 0.(142857) for 1 ÷ 7.
How do I divide by a decimal?
Multiply both numbers by the same power of ten so that the divisor becomes a whole number, then divide as usual. The quotient does not change.
What is the difference between truncating and rounding?
Truncating cuts the digits off at a chosen place. Rounding looks at the next digit and may change the last one. This calculator truncates, because long division produces the digits one at a time.
Why can I not divide by zero?
No number multiplied by zero gives a nonzero dividend, so there is no quotient. The calculator tells you the divisor is 0 instead of showing a result.
Can the calculator show a negative quotient?
Yes, in decimal mode. Whole-number mode with a remainder is limited to a nonnegative dividend and a positive divisor.