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A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix , or base, and they are all different, this article presents rules and examples only for decimal ...
Names and symbols used for integer division include div, /, \, and %. Definitions vary regarding integer division when the dividend or the divisor is negative: rounding may be toward zero (so called T-division) or toward −∞ (F-division); rarer styles can occur – see modulo operation for the details.
Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < | d |. The number q is called the quotient, while r is called the remainder. (For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see division algorithm.)
Divisor. In mathematics, a divisor of an integer also called a factor of is an integer that may be multiplied by some integer to produce [1] In this case, one also says that is a multiple of An integer is divisible or evenly divisible by another integer if is a divisor of ; this implies dividing by leaves no remainder.
The properties involving multiplication, division, and exponentiation generally require that a and n are integers. Identity: (a mod n) mod n = a mod n. nx mod n = 0 for all positive integer values of x. If p is a prime number which is not a divisor of b, then abp−1 mod p = a mod p, due to Fermat's little theorem.
Integer. The integers arranged on a number line. An integer is the number zero (0), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]
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