Question

the smallest number by which 24 must be divided to get a perfect cube is ________​

Answer 1

Here ,

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ2 | 24

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎2 | 12

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎2 | 6

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ 3

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎2 × 2 × 2 × 3

$\therefore$ 24 must be divided by 3 to get a perfect cube

now

$\implies \frac{24}{3} \\ \\ \implies {8} \\ \\ \implies {2³}$

$\boxed{proved}$