The factor tree of 360 is shown. Using its prime-power form, how many factors (divisors) does 360 have?

The leaves give $360=2^3\times 3^2\times 5^1$. Each factor picks a power of 2 (4 choices), of 3 (3 choices) and of 5 (2 choices): $4\times 3\times 2=24$. (Multiplying the exponents gives 6; forgetting the 5 gives 12.)