Finding integer solutions of K for equation floor(A/K) = B

Question

How to find integer solutions of K for equation floor(A/K) = B, in terms of A and B where A and B are non-negative integers?

• What I tried:
• floor(A/K) = B
• then B <= A/K < B + 1
• then BK <= A < BK + K
• but I don't know how to proceed further.

Answer 1

If $\lfloor\frac{A}{K}\rfloor=B$ then $\frac{A}{K} - 1 \leq B \leq \frac{A}{K} + 1$, so $\frac{A}{B+1} \leq K \leq \frac{A}{B-1}$