A room with a length of 270 cm and width 150 cm is to be covered with square tiles. What is the largest size of tiles to be used if no space of the room is to be uncovered

Find the greatest common factor of both numbers:

Factors for 150:

150: 1, 2, 5, 6, 10, 15, 25, 30, 50, 75, 150

Factors for 270:

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The largest number they both have in common is 30, so the largest tile could be 30 cm^2.