An office floor measuring 70m 20cm by 5m 25cm

Question

An office floor measuring 7m 20cm by 5m 25cm is to be covered with squere tiles.Only whole tiles will be used and they are all equal sizes.How many tiles are required to cover the floor?

Answer 1

If you are using whole tiles, and they're square, and the floor measures 720 by 525 cm, the largest tile is the largest common factor of 720 and 525. 525=25*21=3*5*5*7; 720=5*12*12=2*2*2*2*3*3*5. The LCF=15, so the largest tile has a side of 15cm. When we divide 720 and 525 by 15 we get 35 and 48 by taking out 3*5 from each set of factors and multiplying the remaining factors together (5*7 and 2^4*3). Now we know how many tiles will fill the length and width of the room, so the total number of tiles is the product of these: 35*48=1,680 tiles.