Question

find the smallest number by which 8640 must be divided so that the quotient becomes perfect cube

Answer 1

First factorize 8640 (you can do this by repeated division) 
You see that 8640 = 2 * 2 * 2 * 2 * 2 * 2 * 3* 3 * 3 * 5 
i.e. 8640 = 2^6 * 3^3 * 5 
2^6 and 3^3 are perfect cubes, so their product is also a perfect cube. The 
non-cube factor is 5. 
So, the smallest number that you should divide 8640 to get a perfect cube is 5

Answer 2

Answer:

Hence, 5 is the smallest number by which 8640 must be divided, so that the quotient is a perfect cube.