Question

Find the smallest number by which 1152
must be divided so that the quotient became a perfect square

Answer 1

$\sf{\underline{By\:Prime\:Factorization\:of\:1152:}}$

$\sf{\underline{We\:get:}}$

$\begin{array}{r | l} 2 & 1152 \\ \cline{2-2} 2 & 576 \\ \cline{2-2} 2 & 288 \\ \cline{2-2} 2 & 144 \\ \cline{2-2} 2 & 72 \\ \cline{2-2} 2 & 36 \\ \cline{2-2} 2 & 18 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

$\sf{\underline{Here:}}$

2 does not form, a pair of square.

$\sf{\underline{So:}}$

It (2) must be divided by 1152 to make it a perfect square.

$\sf{\underline{Therefore:}}$

$\boxed{\sf{ \frac{1152}{2} = 576}}$

$\sf{\underline{So:}}$

$\boxed{\sf{576 = (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3)}}$

$\implies$ $\sf{ 2 \times 2 \times 2 \times 3}$

$\implies$ $\sf{ 4 \times 6}$

$\implies$ $\sf{ 24}$

$\sf{\underline{Therefore:}}$ The smallest number is 24.

Answer 2

Answer:

24

Step-by-step explanation: