Question

What is the least number by which 10125 should be divided so that the quotient is a perfect cube?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B

3

Given number is 10125

Prime factorization of 10125 is:

$\begin{array}{cc}3& 10125\\ 3& 3375\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$\therefore 10125=3\times 3\times 3\times 3\times 5\times 5\times 5$

By grouping them in triplets, we have a triplet of 3 and a triplet of 5. One 3 left behind.
Clealy, 10125 must be divided by 3 in order to make it perfect cube.

Hence, 3 is the required number.