The number of positive divisors of 50,000 can be determined by finding all the distinct positive integers that divide 50,000 evenly. To do this, we can prime factorize 50,000 and use the exponents of the prime factors to calculate the number of divisors.

Prime Factorization of 50,000:
First, let's find the prime factorization of 50,000. The prime factorization is the expression of a number as the product of its prime factors.

50,000 can be written as 2^5 * 5^4.

Calculating the Number of Divisors:
To determine the number of divisors, we consider the exponents of the prime factors. For a number in the form of a^m * b^n * c^p, where a, b, and c are prime numbers, the number of divisors is calculated as (m+1) * (n+1) * (p+1).

In the case of 50,000, we have 2^5 * 5^4. So, the number of divisors would be (5+1) * (4+1) = 6 * 5 = 30.

Therefore, the correct answer is option 'B' - 30.

Explanation:
- Start by finding the prime factorization of 50,000 as 2^5 * 5^4.
- Calculate the number of divisors using the exponents: (5+1) * (4+1) = 6 * 5 = 30.
- The number of positive divisors of 50,000 is 30.
- Option 'B' is the correct answer.