What will be the smallest number by which 128 must be divided to obtain a perfect cube?

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answer is B.

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Detailed Solution

We need to find the smallest number by which 128 must be divided to obtain a perfect cube.
Factoring 128 with the smallest divisor:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

The number is not a perfect cube as 2 does not occur in triplets.
So, we will divide by 2 on both sides to make a triplet:

1282 = 2 × 2 × 2 × 2 × 2 × 2 × 2 2 = 2 × 2 × 2 × 2 × 2 × 2

Now, it is a perfect cube.
Hence, we divide 128 by 2 to make it a perfect cube.
Therefore, option 2 is correct.

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