Description
For nonzero integer divisor compute remainder as the nonnegative modulo abs(divisor) and quotient=(dividend-remainder)/divisor.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
For nonzero integer divisor compute remainder as the nonnegative modulo abs(divisor) and quotient=(dividend-remainder)/divisor.
When to use this tool
Use Euclidean Remainder One Step Bound when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter dividend, divisor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read quotient, remainder. Use the output convention below.
For nonzero integer divisor compute remainder as the nonnegative modulo abs(divisor) and quotient=(dividend-remainder)/divisor.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dividend | Signed integer dividend in the representation declared below. | Required. Safe integer. |
| divisor | Nonzero integer divisor in the representation declared below. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| quotient | Integer quotient under the stated division rule. | Required. Safe integer. |
| remainder | Remainder under the explicitly selected signed-division convention. | Required. Safe integer. |
{
"input": {
"dividend": -7,
"divisor": 3
},
"output": {
"quotient": -3,
"remainder": 2
}
}Limitations and assumptions
- This is numeric Euclidean division rather than arbitrary-size exact integer text. Signed divisors are supported, but extreme safe-integer operands can still encounter intermediate precision or output-range limits.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Integer Euclidean Quotient Sign Case
Choose remainder in [0,abs(divisor)), then return quotient=(dividend-remainder)/divisor and remainder as exact decimal text.
- Signed Remainder Convention Residual
Return truncatedRemainder=dividend%divisor using truncation toward zero, euclideanRemainder=(r+abs(divisor)) modulo abs(divisor), and residual=truncated-euclidean, all as decimal strings.