Remainder Formula

The remainder is the amount left after a division operation when the dividend is not evenly divisible by the divisor.

Division Algorithm

Dividend = Divisor × Quotient + Remainder

Therefore, Remainder = Dividend − (Divisor × Quotient).

Example

When 29 is divided by 6, the quotient is 4. The remainder is 29 − (6 × 4) = 5.

Important Rule

For positive integer division, the remainder is non-negative and smaller than the divisor. The remainder formula is useful in arithmetic, modular mathematics, programming, and number theory.