There are 13 numbered clotting factors. Each play a different role in coagulation cascade.
Waterfall coagulation cascade method is replaced by the cell based model of coagulation which you can google and see how each factor promotes coagulation.
https://www.ncbi.nlm.nih.gov/books/NBK507850/
One of the most common clotting factor deficiency is Factor 8 and 9, leading to hemophilia.