Prímtényezszorzat

Prímtényezőszorzat is a Hungarian mathematical term that translates to "prime factorization" in English. It refers to the process of expressing a composite number as a product of its prime factors. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that is not prime.

The prime factorization of a number is unique, meaning that any composite number can be expressed as a product of prime numbers in only one way, regardless of the order in which the factors are multiplied. This fundamental property is known as the Fundamental Theorem of Arithmetic. For example, the prime factorization of 12 is 2 × 2 × 3, or 2² × 3. The prime factors are 2 and 3.

The process of finding the prime factorization of a number typically involves repeatedly dividing the number by the smallest prime number that divides it evenly, until the result is a prime number. This prime result is then included in the factorization. For instance, to find the prime factorization of 30: 30 ÷ 2 = 15. 15 is not divisible by 2, so we try the next prime, 3. 15 ÷ 3 = 5. 5 is a prime number. Therefore, the prime factorization of 30 is 2 × 3 × 5.

Prime factorization has numerous applications in mathematics, including finding the greatest common divisor (GCD) and the least common multiple (LCM) of two or more numbers, simplifying fractions, and in number theory. It is a foundational concept taught in elementary mathematics.