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When a solute dissolves, only the surface of the solute comes in contact with the solvent. Therefore, the more the surface area of the solute, the faster it dissolves. This is why sugar powder dissolves faster than chunks of sugar.
When you're dealing with solid and liquid solutes, stirring brings fresh parts of the solvent into contact with the solute and particles are forced to connect.
Amount of solute already dissolved
As the solvent approaches the point where it's saturated, it can hold less and less solute.