Question

In order to make the number 648 as a perfect cube, number of times 3 has to be mutiplied to it is

• A. 2
• B. 3
• C. 4

Answer 1

The correct option is A 2

By prime factorisation,
$\begin{array}{cc}2& 648\\ 2& 324\\ 2& 162\\ 3& 81\\ 3& 27\\ 3& 9\\ & 3\end{array}$

648 = 2$\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 $\times$3
$=2^3\times 3^4$
Here, the exponent of 3 is 4. So, it is not a perfect cube.
In order to make the exponent as a multiple of 3, 648 has to be multiplied with 3 twice.