You want to lay tile in a room of your house. The room is 12 feet by 8 feet. What is the side measure of the largest square tile that you can use to cover the whole floor so there is no overlap or cutting?
1 foot
2 feet
4 feet
8 feet
What is the side measure of the largest square tile that you can use to cover the whole floor so there is no overlap or cutting?
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The largest square tile that can be used to cover the entire room without overlap or cutting would be determined by the greatest common divisor (GCD) of the room’s dimensions, 12 feet and 8 feet.
1. The factors of 12 are: 1, 2, 3, 4, 6, 12.
2. The factors of 8 are: 1, 2, 4, 8.
The largest number that appears in both lists of factors is 4. Therefore, the side measure of the largest square tile that can be used is 4 feet.
This size allows you to use tiles that perfectly fit into both dimensions of the room without any cutting required.