Fundamental Theorem of Arithmetic

Question

The 'Fundamental Theorem of Arithmetic' states that "Every positive whole number can be written as a unique product of primes".

I then thought of the positive whole number 7, but since 1 isn't regarded as a prime, there are no primes that multiply to give 7. Where is fault in thinking?

Answer 1

Consider the set $\{7\}$. It is a finite set of prime numbers. And the product of all elements of that set is $7$. So, yes, $7$ can be written as a finite product of primes (a product with a single factor).

Answer 2

A product of a single number is understood as the number itself. And the product of no number is usually understood as $1$.

Just like a sum can have a single term, or even no term ($0$).