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Question

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

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Solution

2972024860224303121534053135345315551
Prime factors of 9720 =2×2×2×3×3×3×3×3×5
The prime factors 3 and 5 do not appear in group of triplets.
So, 9720 is not a perfect cube.
If we divide the number by 3×3×5, then the prime factorisation of the quotient will not contain 3×3×5=45
9720÷45=2×2×2––––––––×3×3×3––––––––
=216=(6)3
Hence, the smallest number by which 9720 should be divided to get a perfect cube, is 45.

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