How many positive whole numbers divide 360 exactly (including 1 and 360)?

Explanation

1. 01

   Prime factorisation: $360 = 2^3 \times 3^2 \times 5$.

2. 02

   A divisor takes the power of 2 from 0 to 3 (4 ways), of 3 from 0 to 2 (3 ways), of 5 from 0 to 1 (2 ways).

3. 03

   Divisors $= 4 \times 3 \times 2 = 24$.