How can one find the x value that gives the largest possible value to the equation (100floor(10000/(floor(100000/(2x))+1)))/x?

Question

How can one find the x value that gives the largest possible value to the equation

$$\frac{100\left\lfloor\frac{10000}{\left\lfloor \frac{100000}{2x}\right\rfloor+1}\right\rfloor}{x}$$

where $x$ is a whole number, and 100000 is divisible by $x$.

Answer 1

$\frac{\mathrm{10}^{\mathrm{5}} }{{x}}\in{Z}^{+} ,\frac{\mathrm{10}^{\mathrm{2}} \left[\frac{\mathrm{10}^{\mathrm{4}} }{\left[\frac{\mathrm{10}^{\mathrm{5}} }{\mathrm{2}{x}}\right]+\mathrm{1}}\right]}{{x}}\left({MAX}\right) \\ $ $=\frac{\mathrm{10}^{\mathrm{2}} \left(\frac{\mathrm{10}^{\mathrm{4}} }{\frac{\mathrm{10}^{\mathrm{5}} }{\mathrm{2}{x}}−\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}}\right)}{{x}}=\frac{\mathrm{2}.\mathrm{10}^{\mathrm{6}} }{\mathrm{10}^{\mathrm{5}} +{x}} \\ $ $\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\neq\mathrm{0}\Rightarrow{x}=\mathrm{1} \\ $