Question

Find the smallest number by which 128 must be divided to obtain a perfect cube.​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

The prime factorisation of 128 gives:

128 = 2×2×2×2×2×2×2

Now, if we group the factors in triplets of equal factors,

128 = (2×2×2)×(2×2×2)×2

Here, 2 cannot be grouped into triples of equal factors.

• Therefore, we will divide 128 by 2 to get a perfect square.

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Answer 2

Answer:

The prime factorisation of 128 gives:

128 = 2×2×2×2×2×2×2

Now, if we group the factors in triplets of equal factors,

128 = (2×2×2)×(2×2×2)×2

Here, 2 cannot be grouped into triples of equal factors.

Therefore, we will divide 128 by 2 to get a perfect square.

Step-by-step explanation: