Question

Is it possible for a composite number to have more than one prime factorization?Is is possible for a number to have no prime factors why?

Answer 1

Every positive number, except 1, can only have one prime factorization (exchanging the terms of the factorization is still considered as the same factorization). This is the fundamental theorem of arithmetic. 1 has no prime factors since 1 itself is not a prime. One of the reasons that 1 is not a prime because fundamental theorem of arithmetic is more complex when 1 is a prime.