Question

Find the smallest number by which 1715 be divided so that the quotient is a perfect cube.

Answer 1

For a number to be a perfect cube, its prime factors should be expressed as triplets.
By prime factorization, we get $1715=7\times 7\times 7\times 5$

We have three 7’s but only one 5 so we need to divide the number by 5.
$\therefore$ We need to divide it by 5, then it becomes cube of 7 i.e 343