We give some new formulas about factorizations of K-k-Schur functions g (k) λ , analogous to the k-rectangle factorization formula s (k) R t ∪λ = s (k) R t s (k) λ of k-Schur functions , where λ is any k-bounded partition and R t denotes the partition (t k+1−t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions , we can prove that g (k) R t divides g (k) R t ∪λ , and in fact more generally that g (k) P divides g (k) P∪λ for any multiple k-rectangles

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... and any k-bounded partition λ. We give the factorization formula of such g (k) P and the explicit formulas of g (k) P∪λ /g (k) P in some cases.