Question

The smallest number by which 16384 must be divided so that quotient is a perfect cube is:

• A. 2
• B. 4
• C. 12
• D. None of these

Answer 1

The correct option is B

4

The given number, 16384's prime factorisation is :

$\begin{array}{cc}2& 16384\\ 2& 8192\\ 2& 4096\\ 2& 2048\\ 2& 1024\\ 2& 512\\ 2& 256\\ 2& 128\\ 2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ & 2\end{array}$
Therefore, $16384=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
$=2^3\times 2^3\times 2^3\times 2^3\times 2^2$
$\Rightarrow$If the number $16384$ is divided by $2^2=4$, the number obtained is $=2^3\times 2^3\times 2^3\times 2^3$ which is a perfect cube
$\therefore$ Required number is 4.