### Instruction: How many positive divisors does $24$ have?### Response: To find the number of positive divisors of a number, I need to factor it into its prime factors and use a formula based on the exponents of those factors.
I know that $24 = 2^3 \cdot 3^1$, so it has two distinct prime factors: $2$ and $3$.
The formula for the number of positive divisors is to add one to each exponent and multiply them together. So in this case, the number of divisors is $(3 + 1)(1 + 1) = 4 \cdot 2 = 8$.