Integer Integer An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The set of integers consists of zero (), the positive natural numbers (, , , …), also called "whole numbers" or "counting numbers", and their additive inverses (the negative integers, i.e., −1, −2, −3, …). The set of integers is often denoted by a boldface Z ("") or blackboard bold formula_1 (Unicode U+2124 ℤ) standing for the German word "Zahlen" (, "numbers"). The integers form
Square-free integer (that is a integer such that is divisible by the square of every prime factor) and a square-free integer, which are coprime. The square-free factor, called the "square-free part" of the number, is the largest square-free divisor of that is coprime with . The square-free part of an integer may be smaller than the largest square-free divisor. Any arbitrary positive integer can be represented in a unique way as the product of a square and a square-free integer : In this factorization, is the largest divisor of " such that is a divisor of . In summary, there are three