Question

Find the smallest no by which the 101306 must be multiplied so that the product are perfect cube

Answer 1

We write down the prime factors of the number as follows :

101306 = 2 × 37 × 37 × 37

For this number to be a cube the 2 which is a prime factor should also be a cube.

It should be as follows :

2³ × 37³

The smallest number to be multiplied by 101306 is :

2² = 4

When we do this we get :

2³ × 37³ = 405224

∛405224 = 74

Which is a perfect cube.