There are probably too many to count, considering how many rivers there really are in the United States. However, if we reduce the problem to its essence, there are a limited number of major rivers in the U.S., specifically the Mississippi, which flows into the Gulf of Mexico, the Missouri, which flows into the Mississippi, The Ohio, which also joins the Mississippi. The Rio Grande, which also dumps into the Gulf, the Yukon, which cuts across Alaska, and the St' Lawrence, which is th eonly one that could officially be said to dump into a lake- bridging the Atlantic and the Great Lakes, specifically.

I hope this helped!