Method A - write in prime factor form
27648 = 2^10 x 3^3 = 2 x 2^9 x 3^3 = 2x (2^3 x 3)^3 = 2 x 24^3
So if 27648 is divided by 2 the quotient is a cube number
Method B - test the list of cubic numbers to find the biggest factor of 27648
The cubic factors are 1, 8, 27, 64, 216, 512, 729, 1728, 4086, 5832, 13824
Method C - divide by factors starting with 1 until quotient is a cube
27648 / 1 = 27648 fail
27648 / 2 = 13824 = 24^3 correct