The dimensions of a room are 16 meters in length and 8 meters wide. A contractor wants to tile the room using the least number of square tiles. What should the tile dimension be?
To find the least number of square tiles, we need to find the greatest common factor (GCF) of the length and width of the room. The GCF of 16 and 8 is 8. So, we can divide both dimensions by 8 to get the smallest integer values:
16 ÷ 8 = 2
8 ÷ 8 = 1
This means that we can cover the entire room with 2 rows of tiles that are 1 tile wide each. So, the length of each tile should be equal to the length of the room divided by the number of rows of tiles, which is:
16 meters ÷ 2 rows = 8 meters per tile
Similarly, the width of each tile should be:
8 meters ÷ 1 tile = 8 meters per tile
Therefore, the tile dimension should be 8 meters by 8 meters.
To find the tile dimension that will use the least number of square tiles, we need to find the greatest common divisor (GCD) of the room's dimensions.
Step 1: Find the GCD of 16 and 8.
The prime factors of 16 are 2 * 2 * 2 * 2
The prime factors of 8 are 2 * 2 * 2
The common prime factors are 2 * 2 * 2 = 8, which is the GCD.
Step 2: Divide the room dimensions by the GCD.
16 / 8 = 2
8 / 8 = 1
The simplified dimensions are 2 meters in length and 1 meter wide.
Therefore, the tile dimension that will use the least number of square tiles is 2 meters by 1 meter.