Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
675
675
Prime Factorization:
⇒ 675 = 5 × 5 × 3 × 3 × 3
= 33 × 52
There are only two 5’s.
∴ 675 is not a perfect cube.
To make it a perfect cube, we multiply with 5.
⇒ 675 × 5 = 3375
= 5 × 5 × 5 × 3 × 3 × 3
= 33 × 53
= 153 which is a perfect cube
∴ The smallest number by which the number 675 must be multiplied to obtain a perfect cube is 5.
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