What is the process of breaking down a composite number until all of the factors are prime?

The process of breaking down a composite number into its prime factors is referred to as prime factorization. This method involves identifying the prime numbers that, when multiplied together, yield the original composite number.

To perform prime factorization, one typically starts with the composite number and repeatedly divides it by the smallest prime number until the resulting quotient is a prime number. This process continues, factoring out primes until only prime numbers remain. For example, the prime factorization of 60 involves breaking it down into its prime components: 60 = 2 × 2 × 3 × 5, which can also be written as (2^2 \times 3^1 \times 5^1).

Understanding prime factorization is essential because it allows for simplifying fractions, finding the greatest common divisor, and solving many other mathematical problems involving numbers. This process highlights the unique way prime factors combine to form composite numbers, illustrating the fundamental theorem of arithmetic that states every integer greater than 1 either is prime or can be uniquely represented as a product of prime numbers.