The methods used for the purification of organic compounds are fundamentally based on both the nature of the compound and the presence of the impurity. This is because the selection of a suitable purification technique requires understanding not only what the organic compound is (i.e., its physical and chemical properties) but also the type of impurities that need to be removed.

For example, if an organic compound is a solid with a high melting point and the impurity is a low melting solid or a liquid, techniques like sublimation or crystallization could be used, which rely on the differences in physical properties between the compound and the impurity. On the other hand, if the compound needs to be purified from substances with similar boiling points, then a more refined method such as fractional distillation might be employed, relying on slight differences in boiling points. In cases where the compound is mixed with substances that have similar physical properties but different chemical reactivities, chemical methods such as extraction or chromatography could be used, which exploit these chemical differences.

Therefore, the correct answer is:

Option C: nature of compound and presence of impurity.