Question

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

• A. 1
• B. 7
• C. 5
• D. Already a perfect cube

Answer 1

The correct option is C

5

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