Here is quiz 1.
Problem 1 is False. This is because the number 1 is neither prime nor composite.
Problem 2 is False. This is because we can have in which case
but
For example, consider
For problem 3, start by writing the number as a product of primes:
Plainly, any positive divisor of
must have the form
where
or
similarly,
or
;
or
and
or
There are 8 possibilities for
5 for
2 for
and 2 for
This gives us a total of
possible positive divisors.