Long Division Calculator
Divide two whole numbers and see the quotient, remainder and the working.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Long division works a digit at a time, carrying the remainder forward into the next position. The quotient and remainder are the exact answer, while the quotient plus remainder over the divisor is the same number written as a mixed value.
Worked example
calculated with the default values below
Dividend (the number divided) 12,345 · Divisor 12 · Decimal places to continue 4 Quotient (whole part) 1,028 · Remainder 9 · Decimal result 1,028.7500 · Working 1 ÷ 12 = 0; 1 − 0×12 = 1 | 12 ÷ 12 = 1; 12 − 1×12 = 0 | 3 ÷ 12 = 0; 3 − 0×12 = 3 | 34 ÷ 12 = 2; 34 − 2×12 = 10 | 105 ÷ 12 = 8; 105 − 8×12 = 9 · Check: quotient times divisor plus remainder 12,345
Method and assumptions
q = floor(n ÷ d); r = n − q × d; cur₀ = 0; cᵢ = curᵢ₋₁ × 10 + δᵢ; qdᵢ = floor(cᵢ ÷ d); curᵢ = cᵢ − qdᵢ × d Dividend is a nonnegative integer; divisor is a positive integer. Decimal output rounds to 0–12 places. Working lists the first six digit steps; remainder and check use the full input. Long division works a digit at a time, carrying the remainder forward into the next position. The quotient and remainder are the exact answer, while the quotient plus remainder over the divisor is the same number written as a mixed value. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Data sources
The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
q = floor(n ÷ d); r = n − q × d; cur₀ = 0; cᵢ = curᵢ₋₁ × 10 + δᵢ; qdᵢ = floor(cᵢ ÷ d); curᵢ = cᵢ − qdᵢ × d
- n
- dividend (non-negative)
- d
- divisor (≥ 1)
- q
- quotient
- r
- remainder
- cur
- carried remainder after each step
- qd
- quotient digit at each step
- c
- working value after bringing down digit δ
- δ
- digit of n processed at step i
Dividend is a nonnegative integer; divisor is a positive integer. Decimal output rounds to 0–12 places. Working lists the first six digit steps; remainder and check use the full input.
Frequently asked questions
What does the decimal-places setting change?
It controls how many digits after the decimal point appear in the decimal result, up to 12. The whole-number quotient and remainder remain unchanged.
Why are only some of the long-division steps shown?
To keep the result readable, the working shows the first six digit steps when the dividend has more than six digits. An ellipsis marks omitted steps; the quotient, remainder, and decimal result still use the full input.
Which inputs and limits apply to Long Division Calculator?
Use the units shown beside each field. These are form limits, not recommended settings. Dividend (the number divided): 0–1,000,000,000,000; Divisor: 1–1,000,000; Decimal places to continue: 0–12 q = floor(n ÷ d); r = n − q × d; cur₀ = 0; cᵢ = curᵢ₋₁ × 10 + δᵢ; qdᵢ = floor(cᵢ ÷ d); curᵢ = cᵢ − qdᵢ × d Dividend is a nonnegative integer; divisor is a positive integer. Decimal output rounds to 0–12 places. Working lists the first six digit steps; remainder and check use the full input. Long division works a digit at a time, carrying the remainder forward into the next position. The quotient and remainder are the exact answer, while the quotient plus remainder over the divisor is the same number written as a mixed value. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
What is a complete worked example for Dividend (the number divided) = 12,345; Divisor = 12?
Inputs: Dividend (the number divided) = 12,345; Divisor = 12; Decimal places to continue = 4. Calculation: q = floor(n ÷ d); r = n − q × d; cur₀ = 0; cᵢ = curᵢ₋₁ × 10 + δᵢ; qdᵢ = floor(cᵢ ÷ d); curᵢ = cᵢ − qdᵢ × d. Results: Quotient (whole part) = 1,028; Remainder = 9; Decimal result = 1028.7500; Working = 1 ÷ 12 = 0; 1 − 0×12 = 1 | 12 ÷ 12 = 1; 12 − 1×12 = 0 | 3 ÷ 12 = 0; 3 − 0×12 = 3 | 34 ÷ 12 = 2; 34 − 2×12 = 10 | 105 ÷ 12 = 8; 105 − 8×12 = 9; Check: quotient times divisor plus remainder = 12,345.