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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.
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.
SQLAlchemy is an open-source Python library that provides an SQL toolkit (called "SQLAlchemy Core") and an Object Relational Mapper (ORM) for database interactions. It allows developers to work with databases using Python objects, enabling efficient and flexible database access.
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.
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
One must multiply the leftmost digit of the original number by 3, add the next digit, take the remainder when divided by 7, and continue from the beginning: multiply by 3, add the next digit, etc. For example, the number 371: 3×3 + 7 = 16 remainder 2, and 2×3 + 1 = 7. This method can be used to find the remainder of division by 7.
SQL includes operators and functions for calculating values on stored values. SQL allows the use of expressions in the select list to project data, as in the following example, which returns a list of books that cost more than 100.00 with an additional sales_tax column containing a sales tax figure calculated at 6% of the price.
The theorem which underlies the definition of the Euclidean division ensures that such a quotient and remainder always exist and are unique. [ 20 ] In Euclid's original version of the algorithm, the quotient and remainder are found by repeated subtraction; that is, r k −1 is subtracted from r k −2 repeatedly until the remainder r k is ...