Long Division Calculator

Background.

This long division calculator does the one thing most online division tools skip: it shows the actual digit-by-digit long-division algorithm, not just a final answer. Enter 853 ÷ 6 and it walks through exactly what a student is expected to write on paper — bring down the 8, see that 6 goes into 8 once with 2 left over; bring down the 5 to make 25, see that 6 goes into 25 four times with 1 left over; bring down the 3 to make 13, see that 6 goes into 13 twice with 1 left over — arriving at quotient 142 with remainder 1, and reporting every one of those intermediate numbers as real, readable data rather than hiding them behind a single division symbol.

Long division is the standard algorithm for dividing multi-digit whole numbers by hand, and it works one digit of the dividend at a time. At each step, you bring down the next digit of the dividend to join whatever remainder is carried from the previous step, figure out how many times the divisor fits into that running number, write that count as the next digit of the quotient, multiply the divisor by that count, and subtract to find the new remainder to carry forward. The process ends when every digit of the dividend has been brought down, and whatever is left over at that point is the final remainder.

This calculator performs exactly that sequence of steps internally and returns them as a structured layout alongside the final numeric answer: the quotient (how many whole times the divisor divides the dividend), the remainder (what is left over), a flag telling you plainly whether the division came out even, a count of how many digit-steps the algorithm took, and the exact decimal value for cross-checking. No approximation is used anywhere — every quotient digit, every subtraction, and every carried-forward remainder is computed with exact whole-number arithmetic.

Long division sits at the foundation of a huge amount of later mathematics. It is the mechanical process behind converting a fraction to a decimal (numerator divided by denominator, one digit at a time, is exactly long division continued past the decimal point), behind polynomial long division in algebra (which follows the identical bring-down-multiply-subtract structure with terms instead of digits), and behind the Euclidean algorithm for finding the greatest common divisor of two numbers, which repeatedly applies exactly this division-with-remainder operation. Understanding long division well is understanding the division algorithm — the theorem that for any dividend a and positive divisor b, there exist unique whole numbers q (the quotient) and r (the remainder) with a = bq + r and 0 ≤ r < b — in its most concrete, hands-on form.

Whether you're checking a homework problem that specifically requires 'showing your work,' relearning long division as an adult, helping a child with an assignment, or just want to see a division problem worked out digit by digit rather than trusting a black-box answer, this page and the calculator above lay out the complete algorithm for any whole-number dividend and divisor.

What is long division calculator?

Long division is the standard algorithm for dividing a (typically multi-digit) whole number, the dividend, by another whole number, the divisor, producing a whole-number quotient and a remainder. It rests on the division algorithm, a fundamental theorem of arithmetic: for any non-negative integer dividend a and any positive integer divisor b, there exist unique integers q and r such that a = b × q + r and 0 ≤ r < b. The quotient q answers 'how many whole times does b fit into a,' and the remainder r is whatever is left over — always smaller than the divisor, since if it were not, one more whole copy of the divisor would fit in. Long division finds q and r one digit of the dividend at a time: starting from the leftmost (most significant) digit, bring down each digit in turn to join a running remainder, determine the largest whole number of times the divisor fits into that running value, record that as the next digit of the quotient, and subtract the divisor times that digit to find the new running remainder before bringing down the next digit. When the dividend divides evenly, the final remainder is exactly 0; otherwise, the final remainder is the r of the division algorithm, and the decimal expansion of a/b beyond that point can be continued by bringing down zeros indefinitely — which is precisely how a fraction's decimal expansion is computed.

How to use this calculator.

1. 01Enter the dividend — the number being divided — in the first field. It must be a whole number, zero or greater.
2. 02Enter the divisor — the number you are dividing by — in the second field. It must be a positive whole number; it cannot be zero.
3. 03Read the primary result, the quotient — the whole number of times the divisor fits into the dividend.
4. 04Read the remainder — whatever is left over after dividing as many whole times as possible. It is always smaller than the divisor.
5. 05Check the 'divides evenly?' flag to see instantly whether the remainder is exactly zero.
6. 06Read the full long-division layout to see every digit-by-digit step: which digit was brought down, what the running value was, how many times the divisor fit, and what remainder was carried forward.
7. 07Use the decimal quotient if you need the exact value including the fractional part, rather than just the whole-number quotient and remainder.

The formula.

The calculator implements the classical long-division algorithm (OpenStax Prealgebra 2e §1.5), which builds the quotient one digit at a time from the most significant digit of the dividend to the least. Maintain a running value, initially zero. For each digit of the dividend, in order from left to right: multiply the running value by 10 and add the new digit (this is the 'bring down' step — it shifts everything already carried one place value to the left and appends the next digit of the dividend). Then divide the divisor into that running value using ordinary integer division: the whole-number result becomes the next digit of the quotient, and the remainder of that division — the running value minus the divisor times the quotient digit — becomes the new running value, carried forward into the next step. If the very first few digits produce a quotient digit of zero (because the divisor is larger than the leading portion of the dividend seen so far), that leading zero is not written as part of the final quotient, exactly as a human would not write a leading zero before the first significant digit of an answer — but a zero digit that occurs in the interior of the quotient (after a non-zero digit has already appeared) is written normally, because omitting it would silently divide the quotient's place values by a power of ten. After every digit of the dividend has been processed, the running value remaining is the final remainder r, and the digits collected form the quotient q, satisfying the division algorithm's defining identity a = b×q + r with 0 ≤ r < b. This is mathematically identical, digit for digit, to the paper-and-pencil method taught in elementary school: bring down, divide, multiply, subtract, repeat.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax. Prealgebra 2e, §1.5 'Divide Whole Numbers'. Rice University, peer-reviewed open-access textbook — the long-division algorithm, quotient, remainder, and the check-by-multiplication method this calculator implements.
2. [2]NIST Digital Library of Mathematical Functions, §27.1 ('Functions of Number Theory') — divisibility, the division algorithm, and the quotient-remainder identity a = bq + r.
3. [3]Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 6th edition, revised by Heath-Brown and Silverman. Oxford University Press, 2008. §1.1 formally states the division algorithm establishing the unique quotient and remainder for any dividend and positive divisor.