Long Division Calculator
with Step-by-Step Work

What Is Long Division?

Long division is a step-by-step method for dividing large numbers by hand. Rather than producing just an answer, the algorithm breaks the calculation into a repeating cycle — divide, multiply, subtract, bring down — applied digit by digit until every part of the dividend has been processed. The result is a quotient (the answer) and, when the division doesn’t come out evenly, a remainder.

The method is taught in elementary and middle school because it builds a concrete understanding of what division means: how many times one number fits into another, and what is left over. That same logic extends directly into polynomial long division at the high school algebra level, where the dividend and divisor are expressions with variables rather than plain numbers.

How to Do Long Division with Steps

To perform long division manually, follow this sequence for each digit of the dividend:

• Divide: Determine how many times the divisor fits into the current portion of the dividend. Write that number above the division bracket as the next digit of the quotient.
• Multiply: Multiply the digit you just wrote by the divisor. Write the product below the working number.
• Subtract: Subtract the product from the current working number. The result is the partial remainder.
• Bring down: Bring the next digit of the dividend down and append it to the partial remainder. This becomes the new working number.
• Repeat until all digits have been brought down. The final working number is the remainder.

For example, dividing 487 by 32: 32 goes into 48 once (write 1). 1 × 32 = 32; 48 − 32 = 16. Bring down 7 → 167. 32 goes into 167 five times (write 5). 5 × 32 = 160; 167 − 160 = 7. No digits remain, so the answer is 15 remainder 7, or 15 R7.

Long Division Calculator with Steps and Remainders

The calculator on this page performs every step of the algorithm and displays the full working — not just the quotient. When the division doesn’t come out evenly, you can choose to express the result as a remainder (15 R7), a mixed number (15 7/32), or a decimal (15.21875). For decimals, the calculator continues the long division by appending zeros to the remainder until it reaches the specified precision.

Long Division with Decimals

Long division with decimals follows the same divide-multiply-subtract-bring-down cycle. Once the dividend is exhausted, place a decimal point in the quotient and continue by bringing down zeros from the remainder. The process continues until the remainder is zero or the desired number of decimal places is reached. If the remainder repeats, the decimal is repeating (rational).

Polynomial Long Division Calculator

Polynomial long division works identically to numeric long division, but the “digits” are the terms of a polynomial, sorted by descending degree. At each step you divide the leading term of the current expression by the leading term of the divisor, multiply, subtract, and bring down the next term. The AI solver on this page handles polynomial division in full, showing every term-by-term step with plain-language commentary. This is particularly useful for pre-calculus and algebra II students working on rational functions, partial fractions, or the factor theorem.

For problems beyond division — derivatives, integrals, limits, or quadratic equations — use the MathGPT Free AI math solver on the homepage, which covers 12+ math subjects with the same step-by-step format.

Long Division vs. Short Division vs. Synthetic Division

Long division shows every multiplication and subtraction explicitly, making the method transparent and easy to check. Short division is a condensed version that works mentally for small divisors (typically single digits), writing only the quotient digits and carrying remainders mentally. Synthetic division is an efficient shorthand for dividing a polynomial by a linear binomial of the form (x − c); it omits the variable notation and operates purely on coefficients. When to use each:

• Learning or teaching the concept → long division
• Quick mental calculation with a single-digit divisor → short division
• Dividing a polynomial by (x − c) efficiently → synthetic division