Characteristics of numbers and prime factorization?

Answer 1

Each number is either itself a Prime number, or it can be separated into smaller prime numbers. A prime number is a number that has no smaller factors. Factorization into prime factors is unique, except for the order of the factors.

Answer 2

The unique factorisation theorem, also known as the fundamental theorem of arithmetic, states that every positive integer is either a prime or it can be expressed as a product of prime numbers and, in that case, the list of primes, after making allowance for re-ordering, is unque.