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Yes, free glycerol can influence the saponification value of a product. Saponification value is defined as the number of milligrams of potassium hydroxide (KOH) required to saponify one gram of a fat or oil. Glycerol is a byproduct of the saponification reaction, and its presence in the reaction mixture can affect the equilibrium of the reaction. If free glycerol is present, it can react with the KOH, consuming it and reducing the amount available to saponify the fat or oil. This results in a lower saponification value.