By what least number should 675 be multiplied so as to obtain a perfect cube number ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & {\text{5}}\,\,{\text{| 675}} \cr & - - - - - - \cr & 5\,\,|\,\,135 \cr & - - - - - - \cr & 5\,\,|\,\,27 \cr & - - - - - - \cr & 3\,\,|\,\,9 \cr & - - - - - - \cr & 3\,\,|\,\,3\quad \cr & - - - - - - \cr & \,\,\,\,\,|\,\,1 \cr & {\text{Factors are}} \cr & = \,5 \times 5 \times 3 \times 3 \times 3 \cr} $$
∴ It must be multiplied by 5 to make a perfect cube.