Question

What is the least number by which $30375$ should be multiplied to get a perfect cube?

Answer 1

Prime factors of $30375$ are

$3|30375$

__________

$3|10125$

__________

$3|3375$

__________

$3|1125$

__________

$3|375$

__________

$5|125$

__________

$5|25$

__________

$5|5$

_________

$|1$

$=3\times 3\times 3\times 3\times 3\times 5\times 5\times 5$

$=(3\times 3\times 3)\times (5\times 5\times 5)\times 3\times 3$

Clearly, $3-375$ must be multiplied with $3$.