Question

Find the smallest number by which 704 must be divided so that the quotient is a perfect cube​

Answer 1

Solution:

The smallest number that leaves a perfect cube as a quotient when it is divided by 704.

We will derive the prime factorisation of 704,

So,

=> 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11

=> 704 = 2^6 × 11

So we have got, 704 in pair with 2 times the cube of 2 multiplied by 11.

So, we will multiply 704 by 11.