The inductance of a coil is determined primarily by:

The inductance of a coil is indeed influenced by multiple factors that all contribute to its overall effectiveness in storing magnetic energy. The number of turns of conductor is crucial, as increasing the number of turns enhances the magnetic field generated when current flows through the coil, resulting in greater inductance.

The permeability of the core material is another significant factor, as it determines how easily the material can support the formation of a magnetic field. A core with higher permeability will allow the coil to achieve higher inductance due to its ability to concentrate magnetic lines of force within it.

Furthermore, the ratio of the cross-sectional area to the length of the coil also plays a role. A larger cross-sectional area allows for more magnetic flux, while a longer coil may hinder the magnetic field's strength. Therefore, optimizing this ratio is important for maximizing inductance.

Considering that all these elements (number of turns, core material permeability, and the dimensional characteristics of the coil) collectively influence the inductance, selecting the option that encompasses all of these factors reflects a comprehensive understanding of electromagnetic principles. Each factor is essential and interrelated, justifying why "all of the above factors" is the correct answer.