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and −2 is the least absolute remainder. In the division of 42 by 5, we have: 42 = 8 × 5 + 2, and since 2 < 5/2, 2 is both the least positive remainder and the least absolute remainder. In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Banten's 2006 population totaled 9,351,470, with 36.04 percent children, 2.57 percent elderly, and the remainder 15 to 64 years old. The province's 2005 Gross Regional Domestic Product (GDP) was primarily from the manufacturing industry sector (49.75 percent), followed by the trade, hotel and restaurant sector (17.13 percent), transportation ...
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
The largest remainder method divides each party's vote total by a quota. Usually, quota is derived by dividing the number of valid votes cast, by the number of seats. The result for each party will consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
"In arithmetic, the remainder (or modulus) is the amount "left over" after performing the division of two integers which do not divide evenly, that is, where the result of the division cannot be expressed as an integer." does not seem quite right since the remainder could be zero: 8/2 is an integer, 8 divided by 2 has remainder 0.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.