What is the process of breaking down a composite number into prime factors called?

The process of breaking down a composite number into its prime factors is known as prime factorization. This term specifically refers to identifying and expressing a composite number as the product of its prime constituents. For example, the prime factorization of 30 can be expressed as 2 × 3 × 5, where 2, 3, and 5 are all prime numbers.

Prime factorization is crucial for various mathematical concepts, such as simplifying fractions, finding the least common multiple (LCM), and greatest common divisor (GCD) of numbers. The focus on prime numbers is essential because they are the building blocks of all natural numbers, and this method helps to understand the structure and relationships between numbers.

In contrast, while factorization generally refers to breaking down any number into its factors, it does not specifically indicate that those factors must be prime. Prime decomposition might sound similar but is less commonly used in mathematical terminology than prime factorization. Simplification, on the other hand, usually pertains to reducing an expression or fraction to its simplest form rather than breaking down composite numbers into primes. Therefore, prime factorization is the precise and appropriate term for this process.