Question

Find the smallest number by which 304 is to be multiplied to obtain a perfect cube

Answer 1

therefore 304 must be multiplied by 38 to make it a perfect cube

Answer 2

The smallest number by which 304 is to be multiplied to obtain a perfect cube is 1444

Given:

Number 304

To find:

The smallest number by which 304 is to be multiplied to get a perfect cube

Solution:

Note: A perfect cube is a number which can written in form of a³ or a number which is obtained by a number multiplying itself 3 times

To find the smallest number by which 304 is to be multiplied to get a perfect cube, write 304 as product of its prime factors

⇒ 304 = 2 × 2 × 2 × 2 × 19  = 2⁴ × 19      

Now group the above factors as triplets

= (2 × 2 × 2) × 2 × 19

Here one 2 and one 19 is left

To make 304 as a perfect cube we need two 2's and two 19's

we need to multiply 304 with 2²×19²

⇒ 2²×19² = 1444

The smallest number by which 304 is to be multiplied to obtain a perfect cube is 1444

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