Question

Find the smallest number by which $33275$ must be divided so that the quotient is a perfect cube.

• A. $23$
• B. $25$
• C. $26$
• D. $11$

Answer 1

The correct option is B $25$

$33275=5\times 5\times \underset{–}{11\times 11\times 11}$

So We should divide the given number by $25$ to get a perfect because factor of $5$ in the given number is $2$.So make it a perfect cube either we can multiply by $5$ or divide $25$.But we are asked to divide the number. So anser is $25$.

$33275÷25=1331={11}^3$