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Remainder Calculator

Find the remainder after integer division

Remainder Formula

a = bq + r, where 0 <= r < |b|

The remainder is what is left after the divisor is subtracted as many whole times as possible from the dividend.

Note: The divisor cannot be zero. For positive integers, this remainder matches the modulo result.

How Remainders Work

A remainder appears when a number cannot be divided evenly into whole groups. It is the leftover part of integer division.

Dividend

The dividend is the number being divided.

Divisor

The divisor is the number used to split the dividend into groups.

Quotient

The quotient counts how many whole groups fit.

Remainder

The remainder is the leftover amount after the whole groups are removed.

Example: 29 divided by 5 gives quotient 5 and remainder 4, because 29 = 5 x 5 + 4.

Applications of Remainders

Long Division Modulo Arithmetic Divisibility Clock Arithmetic Programming Number Patterns

Frequently Asked Questions

What is a remainder?
A remainder is the amount left over after dividing one integer by another. In a = bq + r, r is the remainder.
Can the divisor be zero?
No. Division by zero is undefined, so a remainder with divisor zero is also undefined.
Is remainder the same as modulo?
They are closely related. For positive integers, the remainder and a mod b are the same. Negative values may differ depending on convention.

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