A Berge $k$-factor in a hypergraph is a generalization of a $k$-factor in a graph. In this paper, we study the problem of determining the values $k$ such that every $λ$-edge-connected $r$-regular hypergraph $\HH$ with $k|V(\HH)|$ even has a Berge $k$-factor. While this problem is completely solved for ordinary graphs, we report that there arises a new upper bound to $k$ based on the rank of $\HH$ for hypergraphs and that it is stronger than the classical upper bound based on the edge-connectivity in most cases.