Question

By which smallest number should 36864be divided so that the quotient is a perfect cube?​

Answer 1

Answer:

The smallest number that should be divided 36864 is 9

Step-by-step explanation:

We can factorize the number 36864, and see the factors that can lead  to the quotient that is a perfect cube,

36864 = 256 x 144  =  2⁸ x 12²  =  2¹² x 9  = 2¹² x  3²

Immediately, we can see that if we divided the 36864, we will be left with 2¹²,

who's cube root is 16.

Hence, this way by simple factorization, we can find the smallest number (9) to divide, to get a perfect cube quotient.