SOLUTION: please help me solve this question :By which smallest number must 8640 be divided so that quotient is a
perfect cube?
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Question 767021: please help me solve this question :By which smallest number must 8640 be divided so that quotient is a
perfect cube?
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
To know the answer, 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.
Check: 8640 / 5 = 1728 which is (12)^3 - a perfect cube.
:)
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