That factor appears when you actually do the quite complex maths that lead to the principle; it's quantum mechanics, and it's not something that can be shown easily.
What is important to note is that this factor [tex]\frac{1}{4\pi}[/tex]is not important. What is important is that the uncertainty [tex]\Delta x\Delta p_x[/tex] is approximately of the order of [tex]\hbar=\frac{h}{2\pi}[/tex], which is a characteristic value that appears in many (most) formulas dealing with quantum mechanics.
