primaarifaktorisoinnin
Primaarifaktorisointi (Finnish for primary factorization) is the representation of a positive integer as a product of powers of prime numbers. The process relies on the Fundamental Theorem of Arithmetic, which states that every integer greater than one can be written uniquely as a product of primes, up to the order of the factors. In primaarifaktorisointi the integer \(n\) is expressed in the form \(n = p_{1}^{e_{1}}\cdot p_{2}^{e_{2}}\cdot \dots \cdot p_{k}^{e_{k}}\) where each \(p_{i}\) is a distinct prime and each exponent \(e_{i}\) is a positive integer.
The prime factorization of 60, for instance, is \(2^{2}\cdot 3^{1}\cdot 5^{1}\).
Algorithms for primaarifaktorisointi vary in complexity. Simple trial division tests divisibility by each prime up to
The exponents in a prime factorization reveal properties of the integer: the sum of the exponents indicates
Primaarifaktorisointi is also a fundamental tool in number theory for defining functions such as the divisor