What is the fewest number of squares needed to cover your 1113 rectangle without overlapping?

To cover a rectangle of dimensions 1113 using squares without overlapping, the fewest number of squares needed is 2. You can use one square measuring 1111 x 1111 and another square measuring 2 x 2 to fully cover the rectangle. This approach efficiently utilizes the area while adhering to the constraint of not overlapping.