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In this work a method based on a topological invariance of rational tanglescommonly used in knot theory determines filling factors in the fractionalquantum Hall effect. The main sustain for this hypothesis are the Schubert'stheorems which treats the isotopic between two knots that are numerators ofnon-equivalent rational tangles. This isotopic allows to deduce a new formulafor all filling factors. Besides, it opens a new perspective for a futureconnection between $N-$particles interaction at different fillings and Berryphase evaluated along torus knots

Determining the filling factors of fractional quantum Hall states using knot theory