How many positive factors of 72 are perfect cubes?
To find the positive factors of 72, I can first prime factorize it as 2^3 * 3^2. Then, any positive factor of 72 must be of the form 2^a * 3^b, where 0 <= a <= 3 and 0 <= b <= 2. To be a perfect cube, a factor must have exponents that are multiples of 3. So, the possible values for a are 0 and 3, and the possible values for b are 0. This means there are only two positive factors of 72 that are perfect cubes: 2^0 * 3^0 = 1 and 2^3 * 3^0 = 8. 