Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
192
192
Prime Factorization:
⇒ 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
= 23 × 23 × 3
There is only one 3.
∴ 192 is not a perfect cube.
Since in factorization, 3 appear only one time, we should divide the number 192 by 3.
⇒ 192 ÷ 3 = 64
= 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23
= 43 which is a perfect cube
∴ The smallest number by which the number 192 must be divided to obtain a perfect cube is 3.
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