Answer:
16
Explanation:
To find the smallest number by which 2304 can be divided so that the quotient is a perfect cube, we need to identify the highest power of each prime factor that can be divided.
The prime factorization of 2304 is:
2304 = 2^7 * 3^2
To make the quotient a perfect cube, we need to divide by the highest power of 2 and 3 that would result in a perfect cube.
The highest power of 2 that can be divided is 2^6 (64), and the highest power of 3 that can be divided is 3^2 (9).
Therefore, the smallest number by which 2304 can be divided so that the quotient is a perfect cube is 64 * 9 = 576.