Long Division Calculator
Divide one whole number by another and see the quotient, the remainder and the long-division working step by step — plus the exact decimal, including the repeating part.
Long division brings down one digit at a time: at each step it finds how many times the divisor fits, writes that digit of the quotient, subtracts, and carries the remainder to the next digit.
How the long division calculator works
Long division brings down one digit at a time: at each step it finds how many times the divisor fits, writes that digit of the quotient, subtracts, and carries the remainder to the next digit. The decimal continues the same process after the point. When a remainder repeats, the decimal repeats from that point onwards — which is why 1 ÷ 3 is 0.333… forever and 1 ÷ 7 repeats in a six-digit cycle.
Formula: dividend = divisor × quotient + remainder, 0 ≤ remainder < divisor
Worked examples
| Inputs | Quotient (whole) | Note |
|---|---|---|
| 1234 ÷ 7 | 176 | 176 remainder 2 |
| 100 ÷ 8 | 12 | 12 remainder 4 — decimal terminates at 12.5 |
| 1 ÷ 3 | 0 | 0.(3) — repeats forever |
| 1 ÷ 7 | 0 | 0.(142857) — a six-digit cycle |
FAQFrequently asked questions
What is the quotient and the remainder?
The quotient is how many whole times the divisor fits; the remainder is what is left over. 1234 ÷ 7 is 176 with 2 left.
Why does 1 ÷ 3 never end?
The remainder repeats, so the same digit is produced forever. The bracket in 0.(3) marks the repeating part.
How long can a repeating cycle be?
Up to one less than the divisor: sevenths repeat every six digits.
When does a decimal terminate?
When the divisor’s only prime factors are 2 and 5 — the base-ten factors. Eighths terminate, thirds do not.
Can I divide negative numbers?
Yes; the sign is applied to the quotient and the working is shown for the absolute values.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.