Question

by which least number 250 × 512 should be divided to make it a perfect cube

Answer 1

$\textbf{Answer}$

$\textbf{The given number is,}$
$\textbf{250}$ × $\textbf{512}$

$\textbf{Lets resolve 250 in prime factors}$,
250 = 2×5×5×5
=> 250 = (2) × (5)^3
So 250 is not a perfect cube.

$\textbf{Lets resolve 512 in prime factors}$,
512 = 2×2×2×2×2×2×2×2×2
=> 512 = (2)^3 × (2)^3 × (2)^3
So 512 is a perfect cube.

$\textbf{Lets comeback to the question}$,

$\textbf{250}$×$\textbf{512}$ = (2) × (5)^3 × (2)^3 × (2)^3 × (2)^3

$\textbf{We can clearly see that,}$
If digit 2 is divided from the term,then it will be a perfect cube all together.

$\textbf{The least number}$ by which $\textbf{250}$×$\textbf{512}$ $\textbf{should be divided}$ to $\textbf{make it perfect cube is 3}$.

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$

Answer 2

\textbf{The given number is,}The given number is, 
\textbf{250}250 × \textbf{512}512 

\textbf{Lets resolve 250 in prime factors}Lets resolve 250 in prime factors ,
250 = 2×5×5×5
=> 250 = (2) × (5)^3
So 250 is not a perfect cube.

\textbf{Lets resolve 512 in prime factors}Lets resolve 512 in prime factors ,
512 = 2×2×2×2×2×2×2×2×2
=> 512 = (2)^3 × (2)^3 × (2)^3
So 512 is a perfect cube.

\textbf{Lets comeback to the question}Lets comeback to the question ,

\textbf{250}250 ×\textbf{512}512 = (2) × (5)^3 × (2)^3 × (2)^3 × (2)^3

\textbf{We can clearly see that,}We can clearly see that, 
If digit 2 is divided from the term,then it will be a perfect cube all together.

\textbf{The least number}The least number by which \textbf{250}250 ×\textbf{512}512 \textbf{should be divided}should be divided to \textbf{make it perfect cube is 3}make it perfect cube is 3 .