A hall floor is 7 m 92 cm long and 5 m 40 cm broad. It is to be paved with identical square tiles of the largest possible size, with no tile cut.
How many tiles are needed?

In centimetres the floor is 792 by 540. The largest square tile has side HCF(792, 540): $792=2^3\times 3^2\times$ 11 and $540=2^2\times 3^3\times$ 5, so HCF = $2^2\times 3^2=36$ cm. The floor then holds 792 / 36 = 22 tiles along the length and 540 / 36 = 15 across the breadth, so $22\times 15=330$ tiles. Answering 36 gives the tile side rather than the count, and 22 counts only one direction.