Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
256
256
Prime Factorization:
⇒ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23 × 22
There are only two 2’s.
∴ 256 is not a perfect cube.
To make it a perfect cube, we multiply with 2.
⇒ 256 × 2 = 512
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23 × 23
= 83 which is a perfect cube
∴ The smallest number by which the number 256 must be multiplied to obtain a perfect cube is 2.
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