George wants to cover a floor measuring 110 cm by 70 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 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
The highest common factor of 70 and 110 is 10.
Largest possible length of the side of each tile = 10 cm
(b)
Number of tiles arranged lengthwise
= 110 ÷ 10
= 11
Number of tiles arranged breadthwise
= 70 ÷ 10
= 7
Number of tiles to cover the floor
= 11 x 7
= 77
Answer(s): (a) 10 cm; (b) 77