Prime factorization is the process of expressing a number as a product of its prime factors. A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. Prime factorization breaks down a composite number into prime numbers that multiply together to give the original number. For example, the number 30 can be factorized as 5 × 6, but since 6 is not prime, it can be further factorized into 2 × 3. Therefore, the prime factorization of 30 is 2 × 3 × 5, where all factors are prime numbers
. There are common methods to find prime factorization:
- Division method: Repeatedly divide the number by the smallest prime number that divides it exactly until the quotient is 1.
- Factor tree method: Break the number into any two factors, then continue breaking down composite factors until all factors are prime
Prime factorization is unique for every number (except for the order of factors), a fact known as the Fundamental Theorem of Arithmetic
. In summary, prime factorization is writing a number as a product of prime numbers that multiply to give the original number, and it is fundamental in various areas of mathematics and applications like cryptography
