What is the process of expressing a number as a product of primes called?

The process of expressing a number as a product of primes is called prime factoring. This method involves breaking down a composite number into its prime factors, which are the basic building blocks of numbers in the field of number theory. Each integer greater than one can be uniquely represented as a product of prime numbers, which is foundational for various areas of mathematics, including cryptography, algebra, and number theory.

For example, considering the number 60, it can be factored into prime numbers as follows: 60 = 2 × 2 × 3 × 5, or expressed as 2² × 3 × 5. This concept allows mathematicians to study the properties of numbers more effectively.

The other terms provided do not correspond to established mathematical processes. There is no recognized method called prime extension, prime listing, or prime classification that pertains to the breaking down of numbers into their prime factors, which reinforces why prime factoring is the correct choice in this context.