Finding Positive Divisors of 240

Consider the number 240. We want to determine which of the following options provides the correct number of positive divisors of this number. To find the number of positive divisors, we need to find its prime factorization first.

The prime factorization of a number can be expressed as:

$$ n = p_1^{e_1} imes p_2^{e_2} imes ext{...} imes p_k^{e_k} $$

where $p_1, p_2, ..., p_k$ are the prime factors and $e_1, e_2, ..., e_k$ are their respective powers. The formula to calculate the total number of positive divisors is:

$$ D(n) = (e_1 + 1)(e_2 + 1) ext{...} (e_k + 1) $$

What is the total number of positive divisors of 240?