Find the smallest number by which 8,232 must be divided to make it a perfect cube. Also, find the cube root of the perfect cube so obtained.

Finding prime factors of 8232

$8232 = (2\times 2 \times 2) \times 3 \times(7 \times 7 \times 7)$

Since the prime factor 3 is not in triplet, so 8,232 must be divided by 3 to make it a perfect cube.

$\dfrac{8232}{3} = 2744$

Finding prime factors of 2744

$\sqrt[3]{2744} = \sqrt[3]{(2\times 2 \times 2) \times(7 \times 7 \times 7)}\\[1em] \sqrt[3]{2744} = \sqrt[3]{2 \times 7}\\[1em] \sqrt[3]{2744} = 14$

2744 must be divided by 3 so that the quotient is a perfect cube. The cube root of 2744 is 14.