Free · Mathematics models
Signed Integer Division and Remainders
Inspect truncating and alternate integer quotient/remainder identities for signed inputs.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this 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.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Dividing 13 by 4 gives an integer quotient of 3 and a remainder of 1: 13 = 3×4 + 1.
The first quotient truncates dividend/divisor toward zero. The second rounds in the opposite direction when negative inputs allow an alternate nonzero remainder.
Worked example
Enter these known values and leave the other values blank.
- Dividend
- 13
- Divisor
- 4
- Quotient
- 3
- Remainder
- 1
Assumptions and limitations
- Use integer operands and a nonzero divisor. The first identity uses a remainder with the dividend’s sign.
- For negative inputs the captured alternate convention uses the other adjacent quotient and its corresponding remainder. Exact divisions do not need a second remainder.
- These formulas calculate results from entered inputs; a missing input can prevent a result.
Common questions
What does this scenario assume?
Use integer operands and a nonzero divisor. The first identity uses a remainder with the dividend’s sign.
What does the result leave out?
For negative inputs the captured alternate convention uses the other adjacent quotient and its corresponding remainder. Exact divisions do not need a second remainder.
References
- Python language reference: contrasting floor-division convention
- Calculation definition and unit reference
Model input requirements: The dividend must be an integer. The divisor must be a nonzero integer.