Question

Find the smallest number by which 3456 must be divided so that the quotient become a perfect cube . find the cube root of the quotient.

Answer 1

2 3456
2 1728
2 864
2 432
2 216
2 108 
2 54
3 27
3 9
3 3
3 1 
3456= 3*3*3*2*2*2*2*2*2*2
number to be divided by= 2
quotient= 3456/2
=1728
cube root=
2 1728
2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
3 1
1728=6*6*6*6*6*6*3*3*3
cube root= 6*6*3
= 108