Primfaktorzerlegung

Primfaktorzerlegung is the decomposition of a positive integer into a product of prime numbers. This process is also known as prime factorization. It is a fundamental concept in number theory, algebra, and mathematics.

The prime factorization of a number can be achieved by repeatedly dividing the number by the smallest prime number until it is no longer divisible, then moving to the next prime number, and so on. The process is stopped when the number is reduced to 1.

The prime factors of a number are unique, and their product is unique. This uniqueness property is a fundamental theorem in number theory. The prime factorization of a number can be used to determine the greatest common divisor (GCD) of two or more numbers.

In mathematics, prime factorization has important applications in various fields, such as cryptography, coding theory, and optimization problems. It is also used in computer science for tasks such as data compression and error detection.

Some examples of prime factorization include:

* The prime factorization of 12 is 2^2 * 3.

* The prime factorization of 36 is 2^2 * 3^2.

* The prime factorization of 60 is 2^2 * 3 * 5.

Prime factorization can be performed using various algorithms, such as the trial division method, the Pollard's rho algorithm, or the general number field sieve.