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<ol class="abc-list"><li data-list-item-id="item-1763492053760-bipr7jpgp" data-list-item-path="item-1763492053760-bipr7jpgp"><ol class="i-list"><li data-list-item-id="subitem-1763492055380-elhdr4h1n" data-list-item-path="item-1763492053760-bipr7jpgp/subitem-1763492055380-elhdr4h1n"><div class="list-item-paragraph">Express \(594\) as a product of its prime factors.</div></li><li data-list-item-id="subitem-1763492056597-1bcyh6580" data-list-item-path="item-1763492053760-bipr7jpgp/subitem-1763492056597-1bcyh6580"><div class="list-item-paragraph">Find the smallest positive integer \(k\) such that&nbsp;\(\frac{594}{\sqrt{k}}\) is a perfect cube.</div></li></ol></li><li data-list-item-id="item-1763492057878-hjhww496t" data-list-item-path="item-1763492057878-hjhww496t"><div class="list-item-paragraph">Megan is playing with \(594\) cubes. Megan uses all \(594\) cubes to make a cuboid.<br></div><div class="list-item-paragraph">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.</div></li><li data-list-item-id="item-1763492141249-xrgarlb7z" data-list-item-path="item-1763492141249-xrgarlb7z"><div class="list-item-paragraph">Each cube has a volume of \(2\) cm³. Calculate the maximum number of cubes that Megan can fit into a box of dimensions \(8\) cm by \(10\) cm by \(10\) cm.</div></li></ol>
<p>For part (c), arrange the cubes in straight rows and layers with their edges parallel to the box edges.</p>

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

Volume and Surface Area of Prisms

Perfect Squares and Cubes Using Prime Factors

Prime Factorisation of Positive Integers

Packing Cubes and Cuboids

Factors, Multiples and Divisibility of Integers

Prime Factorisation and Cube Problems Involving 594

Primes, HCF and LCM

<ol class="abc-list"><li data-list-item-id="item-1758616108085-j1v1h3ffa" data-list-item-path="item-1758616108085-j1v1h3ffa"><ol class="i-list"><li data-list-item-id="subitem-1758616109517-0ilsci5an" data-list-item-path="item-1758616108085-j1v1h3ffa/subitem-1758616109517-0ilsci5an"><div class="list-item-paragraph">Express \(594\) as a product of its prime factors.</div></li><li data-list-item-id="subitem-1758616109900-2k6sh0j0u" data-list-item-path="item-1758616108085-j1v1h3ffa/subitem-1758616109900-2k6sh0j0u"><div class="list-item-paragraph">Find the smallest positive integer \(k\) such that&nbsp;\(\frac{594}{\sqrt{k}}\) is a perfect cube.</div></li></ol></li><li data-list-item-id="item-1758616117977-z7i02uk7r" data-list-item-path="item-1758616117977-z7i02uk7r"><div class="list-item-paragraph">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.</div></li><li data-list-item-id="item-1758616118990-5cgufu51b" data-list-item-path="item-1758616118990-5cgufu51b"><div class="list-item-paragraph">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.</div></li></ol>
<p>For part (c), arrange the cubes in straight rows and layers with their edges parallel to the box edges.</p>

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.

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.

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