Question

What is the least positive integer with which you have to multiply 243 to get a perfect cube?

Answer 1

Resolving 243 into prime factors, we have
243= 3 x 3 x 3 x 3 x 3
Grouping the factors in triplets of equal factors, we get
243 = (3 x 3 x 3) x 3 x 3
Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors 3 x 3.
Therefore, 243 is not a perfect cube.