Question

find the smallest number by which 30375 must be divided so that the quotient becomes a perfect cube also find the cube root of the quotient please write it in step by step

Answer 1

30375=3√3×3×3×3×3×5×5×5

As 3,3 are not tripled so,

3×3 = 9 will be the smallest number which must be divided by 30375 to mate it a perfect cube

When 30375 will be divided by 9 then it will be 3375 and 3375 is a perfect cube of 15.

Answer 2

The Prime Factorization is:

3 x 3 x 3 x 3 x 3 x 5 x 5 x 5

In Exponential Form:

35 x 53

CSV Format:

3, 3, 3, 3, 3, 5, 5, 5

All Factors of 30375:

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 375, 405, 675, 1125, 1215, 2025, 3375, 6075, 10125, 30375

Prime[2] = 3, Prime[3] = 5

so, answer is 3×5=15