Integer Euclidean Quotient Sign Case Tool

Description

Choose remainder in [0,abs(divisor)), then return quotient=(dividend-remainder)/divisor and remainder as exact decimal text.

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.

Choose remainder in [0,abs(divisor)), then return quotient=(dividend-remainder)/divisor and remainder as exact decimal text.

When to use this tool

Use Integer Euclidean Quotient Sign Case 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.

Parse signed decimal-integer dividend and nonzero divisor. Choose remainder in [0,abs(divisor)), then return quotient=(dividend-remainder)/divisor and remainder as exact decimal text.^[1]

Input field	Meaning and units	Accepted input
dividend	Signed integer dividend in the representation declared below.	Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above.
divisor	Nonzero integer divisor in the representation declared below.	Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above.

Output field	Interpretation	Returned shape
quotient	Integer quotient under the stated division rule.	Required. Text; maximum UTF-16 length 8192.
remainder	Remainder under the explicitly selected signed-division convention.	Required. Text; maximum UTF-16 length 8192.

json

{
  "input": {
    "dividend": "-7",
    "divisor": "3"
  },
  "output": {
    "quotient": "-3",
    "remainder": "2"
  }
}

Limitations and assumptions

The quotient follows the Euclidean remainder convention even for negative divisors. It differs from truncating division in many languages; the result satisfies dividend=quotient*divisor+remainder.
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.

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

Calculation and input contract: number/integer-euclidean-quotient-sign-case — tool.io

Similar or alternative tools

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.
Integer Ceiling Division Sign Case
Return exact ceiling quotient and remainder=numerator-quotient*denominator as decimal strings.