Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials

We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes, our formulas generalize the classical hook-length formula and the Littlewood formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its $q$-analogs, which were studied in previous papers of the series.