How many distinct positive factors does 32 have?
Since 32 is a power of 2, its only factors are the powers of 2 less than or equal to it.  These are 1, 2, 4, 8, 16, and 32, so there are $\boxed{6}$ positive factors of 32.
6
Level 2
Number Theory
Problem: How many distinct positive factors does 32 have?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of distinct positive factors of 32, first, recognize that 32 can be expressed as a power of a prime number. Specifically, 32 is equal to 2 raised to the power of 5, or 2^5. 

Next, apply the formula for finding the number of distinct positive factors of a number based on its prime factorization. If a number is expressed as p1^e1 * p2^e2 * ... * pk^ek, where p1, p2, ..., pk are distinct prime factors and e1, e2, ..., ek are their respective positive integer exponents, the number of distinct positive factors is given by (e1 + 1)(e2 + 1)...(ek + 1).

In the case of 32, there is only one prime factor, which is 2, and its exponent is 5. Therefore, we calculate the number of distinct positive factors as follows:

1. Identify the exponent of the prime factor: e1 = 5.
2. Apply the formula: (e1 + 1) = (5 + 1) = 6.

Thus, the total number of distinct positive factors of 32 is 6.<|END_OF_LATENT|> The final answer is $6$.