Question

what is the smallest number by which 864 must multiplied so that the product is a perfect cube ?
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Answer 1

Answer:

Since 2 × 2 is the only in complete triplet, so 864 has to be multiplied by 2 to make it a perfect cube.

Step-by-step explanation:

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Answer 2

Given: A number 864

To find: The smallest number by which 864 must be multiplied to get a perfect cube.

Solution: According to the given question,

We need to find a number which when multiplies with 864 gives a perfect cube as result.

Now, 864 can be expressed as:-

864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

The prime factors can be grouped as :-

864 = (2 x 2 x 2) x 2 x 2 x (3 x 3 x 3)

We observe that, the factors 2 x 2 can not be grouped.

Hence, to make 864 a perfect cube, we need to multiply it by 2.

Perfect cube = 864 x 2 = 1728

Verification:

Prime factorization of 1728 :-

1728 = (2 x 2 x2) x (2 x 2 x 2) x ( 3 x 3 x 3)

Therefore, 2 is the smallest number by which 864 must be multiplied so that the product is a perfect cube.