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 \(\frac{1}{4\pi}\)is not important. What is important is that the uncertainty \(\Delta x\Delta p_x\) is approximately of the order of \(\hbar=\frac{h}{2\pi}\), which is a characteristic value that appears in many (most) formulas dealing with quantum mechanics.
