The question is how many positive divisors do each of the following numbers have:

1) 6

2) 48

3) 100

4) $\displaystyle 2^{n}$

5) $\displaystyle 10^{n}$

6) 0

I understand how to do #1, #2, and #3. For example:

$\displaystyle 6 = 2^1 * 3^1 = (1 + 1) * (1 + 1) = 4$ positive divisors. (which happen to be 1, 2, 3, and 6)

I used the same method (converting each number to a factor of primes in exponential notation, adding 1 to each exponent, and multiplying the exponents) to solve #2 and #3.

I'm not sure where to start on 4, 5, or 6. Could anyone shed some light on the correct method for doing these problems?