Question

find the smallest number by which 6912 must be divided to obtain a perfect cube

Answer 1

6912 = 2×2×2×2×2×2×2×2×3×3×3

=(2×2) (2×2) (2×2) (2×2)(3×3) ×3

=( 2×2 )^4 × ( 3×3 )^1 × 3

now , the required number is 4 . how ?

6912 / 4 = 1728

1728 = ( 12 )^3

hence,

1728 is a perfect cube of 12.

therefore, the smallest required number is 4.

【 hope it helps 】