Can 1 be the greatest common factor?

Answer 1

Yes. If all your numbers can't be divided with the same number, 1 will be the greatest common factor.

Like for instance with 27 and 8. 27 can be divided with 1, 3 and 9, while 8 can be divided with 1, 2 and 4. The greatest common factor of these two numbers is 1.

Answer 2

Yes, and this is in fact often the case.

One example would be the greatest common factor of two prime numbers, since by definition a Prime number's only factors are itself and one.