Question

What is the smallest number by which 8192 must be divided do the question is a perfect cube? Also find the cube root of the quotient so obtained

Answer 1

8640=2 ×2 ×2 ×2 ×2×2×3×3×3×5

Now, forming the triplets , only  5 is extra factor.

therefore, dividing 8640 by 5 ,we get,1728

perfect cube = 1728 = 2×2×2×2×2×2×3×3×3

hence, 

$\sqrt[3]{1728} = {2}^{2} \times 3 = 12$