Long Division Calculator
Adjust the inputs below. Results update as you type.
How it works
Long division works digit by digit from left to right: divide the leading digits by the divisor, multiply back, subtract, bring down the next digit, repeat. Remainder = dividend − (divisor × quotient). For decimal answers, extend with a decimal point and zeros. Learning long division builds number sense; the algorithm generalizes to polynomial division in algebra.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Long division finds a quotient and remainder step by step: divide, multiply, subtract, and bring down the next digit, repeating until no digits remain.
Worked example
752 ÷ 6 = 125 remainder 2, because 6 × 125 = 750 and 752 − 750 = 2.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
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Frequently asked questions
What are the parts of a division problem?+
The dividend is divided by the divisor to give a quotient, with any leftover as the remainder.
How do I handle a remainder?+
Leave it as a remainder, write it as a fraction (remainder/divisor), or continue with decimals by adding zeros after the decimal point.
Why learn long division?+
It builds number sense and handles divisions too large to do mentally, showing exactly how the quotient is formed.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.