CALCULATE WITH CONFIDENCE

Arithmetic Operations

Floor Division Calculator

Divide signed integers using the floor convention and verify the resulting quotient and remainder.

Exact arithmetic

Find the floor quotient

Signed integer convention

Floor quotient

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter a signed integer dividend.
  2. Enter a nonzero signed integer divisor.
  3. Read the floor quotient and verify the remainder identity.

Calculation method

The quotient is rounded toward negative infinity

Floor division selects q = floor(a/b), not merely the integer obtained by truncating toward zero.

The remainder is r = a − bq. It is zero or has the divisor's sign, and its magnitude is smaller than the divisor's magnitude.

Worked example

Floor-divide −7 by 3

Because floor(−7/3) is −3, the remainder is 2 and reconstructs the dividend.

−7 = 3 × (−3) + 2

Supported inputs

Precision and limits

Integers only

Decimal values are outside this calculator's domain.

Nonzero divisor

Division by zero is undefined and is rejected.

Large exact values

Each input and result component may contain up to 2,000 digits.

Signed convention

The remainder is zero or has the same sign as the divisor.