A rectangular room measures 4 meters 37 centimeters in length and 3 meters 23 centimeters in width. If the floor is to be covered completely with square tiles of the largest possible size without cutting, how many such tiles will be needed?

Explanation

First, convert the dimensions to centimeters: length = 437 cm, width = 323 cm. The side length of the largest square tile is the highest common factor (HCF) of 437 and 323, which is 19 cm. The number of tiles required = (length × width) ÷ (side of tile)² = (437 × 323) ÷ (19 × 19) = 391.