HCF stands for Highest Common Factor, which is the largest positive integer that divides two or more numbers without leaving any remainder. HCF helps in finding the minimum number of tiles to cover the floor by finding the greatest size of each square tile that can fit both the length and breadth of the floor without any gaps or overlaps.
For example, suppose the floor of a room is 8 m 96 cm long and 6 m 72 cm broad. To find the minimum number of square tiles of the same size needed to cover the entire floor, we have to find the HCF of 896 cm and 672 cm (since 1 m = 100 cm). The HCF of 896 and 672 is 224, which means that the length of each square tile is 224 cm. Therefore, the minimum number of square tiles needed to cover the floor is:
Area of the floor / Area of a square tile = (896 x 672) / (224 x 224) = 12
Hence, we need 12 square tiles of size 224 cm x 224 cm to cover the entire floor.