Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
704
704
Prime Factorization:
⇒ 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11
= 23 × 23 × 11
There is only one 11.
∴ 704 is not a perfect cube.
Since in factorization, 11 appear only one time, we should divide the number 704 by 11.
⇒ 704 ÷ 11 = 64
= 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23
= 43 which is a perfect cube
∴ The smallest number by which the number 704 must be divided to obtain a perfect cube is 11.
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