1 used to be considered a prime but it needs excluding from the primes because otherwise the Fundamental Theorem of Arithmetic which says that every integer greater than 1 can be expressed uniquely as a product of primes wouldn't work. E.g. 10 = 2 x 5 is unique, but if 1 were a prime you could also have 10 = 1 x 2 x 5 or 10 = 1 x 1 x 2 x 5 and so on.
The 'prime numbers have two distinct factors but 1 only has one' is a definition deliberated fudged to exclude 1.
I knew someone would know the real reason haha
Thank you noblegiraffe for the thread!