Find exact signed integer quotients and remainders, compare Euclidean and truncation conventions and inspect long-division steps.
01 / PURPOSE-SPECIFIC INPUTS
02 / RESULT & INTERACTIVE INSPECTION
1 ÷ 5 → digit 0 1 − 0 = 1
Magnitude step 1: bring down 1, divide partial 1 to write digit 0, then subtract 0; remainder 1. Final euclidean result: q = 3, r = 2.
| Bring down | Partial dividend | Quotient digit | Subtract | Magnitude remainder |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 |
| 7 | 17 | 3 | 15 | 2 |
| Convention | Quotient | Remainder | Identity |
|---|---|---|---|
| Euclidean | 3 | 2 | 17 = (5) × (3) + (2) |
| Truncation | 3 | 2 | 17 = (5) × (3) + (2) |
| Floor | 3 | 2 | 17 = (5) × (3) + (2) |
| Language / example | Explanation |
|---|---|
| Python integer operands | // and % use floor division: quotient toward −∞; a nonzero remainder has the divisor’s sign. |
| JavaScript Number integer operands | Math.trunc(a / b) and % express truncation-style semantics for safely representable integers. Numbers are floating-point, not unlimited-precision integers; this calculator uses BigInt with a 60-digit operand limit. |
| −17 ÷ −5 | Python: q = 3, r = −2. JavaScript safe integer Number calculation: q = 3, r = −2. Euclidean convention: q = 4, r = 3. Every convention preserves dividend = divisor × quotient + remainder. |
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Integer division expresses a dividend as divisor × quotient + remainder. The quotient and remainder depend on the signed division convention: Euclidean division keeps the remainder nonnegative and smaller than the absolute divisor; truncation takes the quotient toward zero and gives a nonzero remainder the dividend’s sign; floor division takes the quotient toward negative infinity and gives a nonzero remainder the divisor’s sign. Every convention preserves the same division identity. The calculator uses exact integer arithmetic, rejects a zero divisor and decimal operands, and shows magnitude long division followed by the selected sign adjustment.
Find exact signed integer quotients and remainders, compare Euclidean and truncation conventions and inspect long-division steps. Inspect the calculated data through labeled controls and review worked assumptions before using a result.
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The quotient is 3 and the remainder is 2 because 17 = 5 × 3 + 2. The integer division identity is checked through exact integer arithmetic.
The remainder is always at least zero and smaller than the absolute divisor. The quotient adjusts to preserve dividend = divisor × quotient + remainder, even with a negative divisor.
Truncation rounds the quotient toward zero, so a nonzero remainder has the dividend’s sign. For −17 divided by 5 it gives q = −3 and r = −2, while Euclidean division gives q = −4 and r = 3.
No. This tool performs integer quotient-and-remainder division. Scaling decimal operands changes what a remainder represents; the existing Division Calculator supports exact decimal division and explains its scaling.
The digit walkthrough divides absolute magnitudes. The final signed-convention adjustment is shown separately in the exact original-operand identity, so a negative-dividend Euclidean remainder is not confused with the unsigned intermediate remainder.
Each operand may be a signed integer of up to sixty digits, and the divisor cannot be zero. BigInt arithmetic preserves integers beyond ordinary floating-point precision; the displayed walkthrough can be scrolled for wide numbers.