Free · Mathematics models

Integer Euclidean and Signed Remainders

Compare the nonnegative Euclidean residue with captured signed remainder alternatives for positive or negative divisors.

Calculator inputs

Loading calculator…

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

The Euclidean remainder of −17 divided by 5 is 3, while the truncating signed alternative is −2.

Choose the unique residue from zero through abs(divisor)−1; signed alternatives use their captured floor or ceiling quotient.

Enter these known values and leave the other values blank.

Dividend and divisor are exact integers and the divisor is nonzero. The main output is the nonnegative Euclidean residue for either divisor sign.
The two alternative captured branches illustrate quotient-convention differences; programming languages can use different signed rules.
Fractional inputs and complex numbers are outside this integer model.
Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.

Dividend and divisor are exact integers and the divisor is nonzero. The main output is the nonnegative Euclidean residue for either divisor sign.

Fractional inputs and complex numbers are outside this integer model.

Model requirements: Dividend must be an exact integer. Divisor must be a nonzero exact integer.