Question

Find the least number by which 65856 should be divided to make it a perfect cube​

Answer 1

the least no. by which 65856 should be divided to make it perfect cube is 3

...ur answer is 3

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Answer 2

Step-by-step explanation:

$\begin{array}{c | c }2& 65856 \\ \cline{2-2} 2 & 32928 \\ \cline{2-2} 2 & 16464\\ \cline{2-2} 2 & 8232 \\ \cline{2-2} 2 & 4116 \\ \cline{2-2} 2 & 2058 \\ \cline{2-2} 3 & 1029 \\ \cline{2-2} 7 & 343 \\ \cline{2-2} 7 & 49 \\ \cline{2-2} & 7\end{array}$

Therefore, 65856 = 2 x 2 x 2 x 2 x 2x 2x 3 x 7 x 7 x 7

= ( 2² x 7)³ x 3 = 2⁶ x 7³ x 3

Dividing the number by 3 makes it a perfect cube.

Thus, $\frac{65856}{3}$ = $\frac{(2^2 \times 7)^3}{3}$

= (2² x 7)³ = 28³

Hence, the required least number is 3

Cube root of the product of numbers

Find the cube root of the product of two or more numbers, first find the cube root of each number and then find their product.

Alternatively , first find the product of the numbers and then determine its cube root