Faktoroj

Faktoroj is the Esperanto term for factors. In mathematics, a factor of a positive integer n is a positive integer d such that n is divisible by d with no remainder (d divides n). The full set of faktoroj of n are its divisors. For any n greater than 1, 1 and n are factors; the proper divisors of n are its positive divisors excluding n.

Prime factorization is a central concept related to faktoroj. Every integer greater than 1 can be written as a product of prime factors, and this representation is unique up to the order of the factors (the Fundamental Theorem of Arithmetic). For example, the prime factorization of 60 is 2^2 × 3 × 5, and its faktoroj include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

In addition to listing divisors, Faktoroj support several useful operations. The greatest common divisor (gcd) of two numbers can be derived from their shared factor structure, and the least common multiple (lcm) uses the combination of prime factors with appropriate exponents. The divisor function counts how many faktoroj a number has, and plays a role in various number-theoretic problems.

Common methods to find factorization include divisibility tests, constructing a factor tree, or performing prime factorization directly. For large numbers, sieving techniques or computational algorithms help enumerate divisors efficiently.

See also: divisibility, divisors, prime factorization, gcd, lcm, divisor function.

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