Question

THE SMALLEST number by which 16 should be divided to make it a perfect cube is​

Answer 1

THE SMALLEST number by which 16 should be divided to make it a perfect cube is​ 2

Given:

Number: 16

To find:

The smallest number by which 16 should be divided to make it a perfect cube

Solution:

Prime factorizing​ 16, we get

16 = 2 x 2 x 2 x 2

   = 2^4

For a number to be a perfect cube, it should only contain terms with power of either 3 or a multiple of 3, in its prime factorization.

For the number 16, it contains a total of 4 2's, but for this number to be a perfect cube the number of 2's should be in a multiple of 3. Hence, if we divide this number by 2, the number of 2's in the resulting number will be 3, which will satisfy the condition for a number to be a perfect cube.

Therefore,

16 = 2^4

Dividing 16 by 2,

16/2 = 8 = 2 x 2 x 2

             = 2^3

Number 8 contains 3 2's (multiple of 3) and hence is a perfect cube.

Therefore,

16 should be divided by 2 to make it a perfect cube

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