Question

find the smallest number by which 2096 must be divided so that the quotient is a perfect cube​

Answer 1

Answer:

Required smallest number is 262.

Explanation:

Let the required smallest number be a and the number whose perfect cube is ( 2096 / a ) be b.

So,

= > Cube of b = Result on dividing 2096 by a.

= > b^3 = 2096 / a

= > b^3 x a = 2096

Now,

Factors of 2096 = 2 x 1048 = 2 x 2 x 524 = 2 x 2 x 2 x 262 = 2^3 x 262

Thus,

= > b^3 x a = 2^3 x 262

Comparing both sides :

= > b^3 = 2^3 & a = 262

Hence the required smallest number is 262.