Question

The smallest number by which 1080 should be divided to make it a perfect cube is

• A. $3$
• B. $4$
• C. $5$
• D. $2$

Answer 1

The correct option is C $5$

Prime factorisation of $1080$ is
$\begin{array}{cc}2& 1080\\ 2& 540\\ 2& 270\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$

$1080=2\times 2\times 2\times 3\times 3\times 3\times 5=2^3\times 3^3\times 5$

Here, the exponent of 5 is not 3. So, we divide 1080 by 5 to make it a perfect cube

$\Rightarrow \frac{1080}{5}=2^3\times 3^3=(2\times 3{)}^3=6^3$