The correct answer is A) The width of the tank. The free surface correction is a factor used to account for the effect of free surfaces of liquids (such as in tanks) on a vessel's stability. The width of the tank has the greatest effect on the value of the free surface correction because the free surface effect is proportional to the moment of inertia of the free surface, which is primarily determined by the width of the tank. A wider tank will have a larger moment of inertia and thus a greater free surface effect, resulting in a larger free surface correction. The length and draft of the vessel, as well as the specific gravity of the liquid, also play a role in the free surface correction, but their effect is less significant compared to the tank width.