A factory manufactures small metal bolts which are packed for export. One shipment contains \(3072\) bolts. For quality control, the bolts must be repacked into identical cubical boxes, where each box contains the same number of bolts. The arrangement inside each box forms a perfect cube. No bolt is allowed to remain unused
To meet these conditions, the factory supervisor is permitted to add the minimum possible number of bolts to the shipment.
Based on the above scenerio, answer the questions.
Questions:
a) Write \(3072\) as a product of prime factors:
[Note: Enter the product of primes in increasing order.]
b) Find the smallest number by which \(3072\) must be multiplied so that the product becomes a perfect cube:
c) The obtained perfect cube is: