Faktorov

Faktorov is the genitive plural form of the Slovak noun faktor, meaning factors in mathematical and related contexts. In general usage, a factor (faktor) of a number is a number that divides that number exactly, leaving no remainder. If a and b are integers and b = a · c for some integer c, then a is a factor of b. The positive factors of a number include 1 and the number itself; prime numbers have exactly two distinct positive factors, 1 and the prime.

Factorization is the process of expressing a number as a product of its factors. In the integers, every positive integer greater than 1 has a unique prime factorization (up to the order of factors), a statement known as the Fundamental Theorem of Arithmetic. For example, 360 = 2^3 · 3^2 · 5. Methods for finding factors include trial division, the sieve of Eratosthenes, and more advanced algorithms for large numbers, such as Pollard’s rho.

In algebra, factoring a polynomial means writing it as a product of polynomials with lower degree. For instance, x^2 − 5x + 6 factors as (x − 2)(x − 3). The greatest common factor (GCF) of several expressions is the largest factor that divides all of them.

Outside pure mathematics, the term factor also appears in statistics and everyday language, for example as “risk factors” or “contributing factors” for a condition. The Slovak term faktorov is frequently encountered in mathematical writing and in phrases requiring the genitive plural form.