Find the smallest number by which 2560 must be multiples so that the product is a perfect cube.

Let’s find out the prime factors of the given number,


2



2560



2



1280



2



640



2



320



2



160



2



80



2



40



2



20



2



10



5



5




1



∴ 2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5


As we can see, to make the pair of 4 triplets two 5 are required, which is 5×5.


So, 25 will be the number multiplied to 2560, to get the perfect cube.


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