What would happen if 1 was considered a prime number

Question

How would the fundamental theorem of arithmetic be affected if 1 was a prime number?

Answer 1

If 1 was considered as prime, then prime factorization of positive integers would not be unique.

 

   For example, 6 could be written as (2)(3) (a product of 2 prime factors), or as (2)(3)(1) (a product of 3 prime factors).

 

 

 

 

Answer 2

The Fundamental Theorem of the Algebra has nothing to do with prime numbers.