MCQ
Tick $(\checkmark)$ the correct answer: By what least number should $1536$ be divided to get a perfect cube$?$
- A$3$
- B$4$
- ✓$6$
- D$8$
✓
Answer
Correct option: C.
$6$
Factorising $1536,$
We get,
$\begin{array}{c|c}2&1536\\\hline2&768\\\hline2&384\\\hline2&192\\\hline2&96\\\hline2&48\\\hline2&24\\\hline2&12\\\hline2&6\\\hline3&3\\\hline&1\end{array}$
$1536=2\times2\times2\times2\times2\times2\times2\times2\times2\times3$
$=2^3\times2^3\times2^3\times3$
We see that $3$ is left
$\therefore$ In order to get a perfect cube, we should divide it by $3.$
We get,
$\begin{array}{c|c}2&1536\\\hline2&768\\\hline2&384\\\hline2&192\\\hline2&96\\\hline2&48\\\hline2&24\\\hline2&12\\\hline2&6\\\hline3&3\\\hline&1\end{array}$
$1536=2\times2\times2\times2\times2\times2\times2\times2\times2\times3$
$=2^3\times2^3\times2^3\times3$
We see that $3$ is left
$\therefore$ In order to get a perfect cube, we should divide it by $3.$
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