In arithmetic, the remainder (or residue) is the amount "left over" after the division of two integers which cannot be expressed with an integer quotient.

The general form of a linear equation can be expressed as a = q × d + r. In this equation, q can be referred to as the quotient and d as the divisor, while r as the remainder. The equation can be transformed to find the remainder as: r = a - q × d. However, a and d must be natural numbers, with d being non-zero. The quotient is the integer result (rounded down) of the division of a by d. The remainder must also be an integer.

Read more about Remainder:  The Remainder For Natural Numbers, The Case of General Integers, The Remainder For Real Numbers, The Inequality Satisfied By The Remainder, Quotient and Remainder in Programming Languages

Other articles related to "remainder":

Short Division - Modulo Division
... Unsourced material may be challenged and removed When one is only interested in the remainder of the division, this variation on short division ignores the quotient and tallies only remainder digits ... For example, what is the remainder of 16762109 divided by 7? The remainder is zero, so 16762109 is divisible by 7 ... we know that 27 is 21+6 (or 28-1) so we find the intermediate remainder digit is 6, without needing to write the quotient 3 ...
Climate Of Florida - Fog
... Like the remainder of the Southeastern United States, Florida has a winter maximum in dense fog conditions ... Unlike the remainder of the region, the maximum in Florida contains roughly half of the annual occurrences per year, on average ... Its summer minimum is less than the remainder of the Southeast ...
Short Division - Example
... leftmost digit of the dividend, and we write the remainder (1) as a small digit (or digits) to the above and to the right of the partial dividend (9) Next we repeat step 2, using the small ... (4), we write the results as before the quotient above the next digit of the dividend, and the remainder to the right ... (Here 15 divided by 4 is 3, with a remainder of 3.) We repeat step 2 until there are no digits remaining in the dividend ...
Quotient and Remainder in Programming Languages
... With two choices for the inequality, there are two choices for the remainder, one negative and the other positive ... In number theory the positive remainder is chosen by convention ... not, and different languages have adopted different conventions C99 and Pascal choose the remainder with the same sign as the dividend a ...
Remainder (disambiguation)
... Remainder is the amount "left over" when dividing two integers ... Remainder may also refer to Remaindered book, a publisher liquidating the remaining unsold copies of a book Remainder (law), in property law, a future interest created in a ...

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