Question

Find the smallest number by which 675 must be multiplied to obtain a perfect cube.

Answer 1

By resolving 675 into prime factor,


675 = 3×3×3×5×5
By grouping the factors in triplets of equal factors,
675 = (3×3×3)×5×5
Here, 5 cannot be grouped into triplets of equal factors.
∴ We will multiply 675 by 5 to get perfect cube.