Charlie wants to cover a floor measuring 650 cm by 400 cm with square tiles of the same size. Given that he uses only whole tiles, find
- the largest possible length of the side of each tile.
- the number of tiles that are needed to cover the floor.
(a)
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factors of 650: 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650
The highest common factor of 400 and 650 is 50.
Largest possible length of the side of each tile = 50 cm
(b)
Number of tiles arranged lengthwise
= 650 ÷ 50
= 13
Number of tiles arranged breadthwise
= 400 ÷ 50
= 8
Number of tiles to cover the floor
= 13 x 8
= 104
Answer(s): (a) 50 cm; (b) 104
