Question

What is the smallest number by which 2 560 must be multiplied so that the product is a perfect cube

Answer 1

on prime factorization we get
2560=2×2×2×2×2×2×2×2×2×5
but to get a perfect cube we need triplets of prime number(like 2×2×2 or 5×5×5)
in the factors of 2560 ,2 occurs in triplets three times but 5 does not,so to get a triplet of 5 we need to multiply it by 5 two times.
∴5×5=25 should be multiplied to 2560to get a perfect cube.