A warehouse stores wooden blocks packed in a large crate. The total number of blocks in the crate is 5184. For transportation, the blocks must be repacked into identical cubical boxes, such that each box contains the same number of blocks and no block is left over. To achieve this, the supervisor decides to divide the total number of blocks by the smallest possible number so that the resulting number of blocks forms a perfect cube.
Based on this situation, answer the following questions.
(a) Find the prime factorisation of 5184:
[Note: Enter the product of primes in increasing order.]
(b)Find out the smallest number by which 5184 should be divided so that the quotient becomes a perfect cube:
(c) The perfect cube obtained is: