A clear answer before the details
Long division repeatedly finds how many times the divisor fits, multiplies, subtracts, and brings down the next digit. The final remainder must be smaller than the divisor.
Learn long division with a visible method
This long division calculator with steps keeps the written algorithm close to the answer. Long division repeats four actions: estimate how many times the divisor fits, multiply, subtract, and bring down the next digit. The quotient records the whole groups and the remainder is what is left. That makes the tool useful for checking homework, teaching place value, and understanding why a division answer is not always a whole number.
Decimals, remainders, and polynomial long division
Use long division with decimals when you need to continue after a remainder: append a zero to the dividend and continue the same cycle. For example, 7 ÷ 4 = 1 remainder 3 = 1.75. A polynomial long division calculator applies the same leading-term, multiply, subtract, and bring-down idea to expressions instead of numbers; this page focuses on numeric division, while the displayed structure helps learners recognise the shared algorithm.
Formula guide
The key equations are separated below. Start with the calculator mode, then choose the shape or model that matches your problem.
Division identity
The remainder must be smaller than the absolute divisor.
Decimal quotient
Continue after a remainder by bringing down zeroes.
Quotient and remainder
q counts complete groups and r is what remains.
Decimal from a remainder
The remainder becomes a fraction of the divisor.
Worked example
For 1,234 ÷ 12, 12 fits into 12 once, then into 3 zero times, and into 34 twice. The quotient is 102 and the remainder is 10.
Formulas for common use cases
Use the matching equation for the problem you are solving, then enter its variables in the calculator above.
Whole-number division
Use q for complete groups and r for what remains.
Convert a remainder to decimals
The remainder 3 becomes 30 tenths, then the division continues.
Check the answer
Multiply the divisor by the quotient and add the remainder.
How to use this calculator
- Enter the dividend and divisor.
- Press Calculate or use Enter.
- Read the quotient, remainder, and decimal form.
- Copy the complete step list for homework or notes.
Where it helps
Long division is useful when a problem requires a written method, a remainder, or a decimal carried beyond the original digits. It supports negative numbers by applying the sign after dividing absolute values, so the working remains easy to follow. The result panel keeps the important answer visible while the steps explain how each digit was produced.
Common mistakes
Division by zero is undefined. Make sure the divisor is not zero and do not confuse the quotient with the remainder. When a decimal answer continues, trailing zeroes may be added to the dividend without changing its value. A remainder is not another quotient digit unless you continue the process with decimal places.