IP1U1 HOT Q1

1. 1. Express \(594\) as a product of its prime factors.
   2. Find the smallest positive integer \(k\) such that \(\frac{594}{\sqrt{k}}\) is a perfect cube.
2. Megan is playing with \(594\) cubes. Megan uses all \(594\) cubes to make a cuboid. Each of the sides of the cuboid is made up of more than \(3\) cubes. Find the number of cubes on each side of the cuboid.
3. Each cube has a volume of \(2\)cm\(^{3}\). Calculate the maximum number of cubes that Megan can fit into a box of dimensions \(8\)cm by \(10\)cm by \(10\)cm.

For part (c), arrange the cubes in straight rows and layers with their edges parallel to the box edges.