Does the product of two primes only have those primes, itself, and 1 as factors?

Question

Happened to review RSA key generation today, and it has led me to this question. I've tried it with a few but obviously that doesn't make it mathematically proven.

Answer 1

This is trivially true. If a and b are prime, then by definition, which you should know, each has only itself and 1 as factors. Therefore ab only has a and b and 1 as factors.