Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
81
81
Prime Factorization:
⇒ 81 = 3 × 3 × 3 × 3
= 33 × 3
There is only one 3.
∴ 81 is not a perfect cube.
Since in factorization, 3 appear only one time, we should divide the number 81 by 3.
⇒ 81 ÷ 3 = 27
= 3 × 3 × 3
= 33 which is a perfect cube
∴ The smallest number by which the number 81 must be divided to obtain a perfect cube is 3.
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.