Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
128
128
Prime Factorization:
⇒ 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23 × 2
There is only one 2.
∴ 128 is not a perfect cube.
Since in factorization, 2 appear only one time, we should divide the number 128 by 2.
⇒ 128 ÷ 2 = 64
= 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23
= 43 which is a perfect cube
∴ The smallest number by which the number 128 must be divided to obtain a perfect cube is 2.
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