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":

... 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 ...

... 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 ...

... 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 ...

**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 ...

### Famous quotes containing the word remainder:

““What have I gained?”

“Experience,” said Holmes, laughing. “Indirectly it may be of value, you know; you have only to put it into words to gain the reputation of being excellent company for the *remainder* of your existence.””

—Sir Arthur Conan Doyle (1859–1930)

“Then I had only prisoners’ thoughts. I awaited the daily walk which I took in the yard, or my lawyer’s visit. I managed the *remainder* of my time very well. I have often thought that if I was made to live in a dry tree trunk, without any other occupation but to watch the flower of the sky above my head, I would have gradually gotten used to it.”

—Albert Camus (1913–1960)

“There are only three kinds of people: those who serve God, having found him; others who are occupied in seeking him, not having found him; while the *remainder* live without seeking him and without having found him. The first are reasonable and happy; the last are foolish and unhappy; those between are unhappy and unreasonable.”

—Blaise Pascal (1623–1662)