Haden wants to cover a floor with square tiles the same size the floor measures 315 inches by 108 inches of she uses only whole tiles,find the greatest possible length of each tile;
GCD(315,108) = 9
To find the greatest possible length of each tile, we need to find the greatest common divisor (GCD) of the two dimensions of the floor: 315 inches and 108 inches.
We can use the Euclidean algorithm to find the GCD:
Step 1: Divide the larger dimension by the smaller dimension.
315 ÷ 108 = 2 remainder 99
Step 2: Divide the previous divisor (108) by the remainder (99).
108 ÷ 99 = 1 remainder 9
Step 3: Divide the previous divisor (99) by the remainder (9).
99 ÷ 9 = 11 remainder 0
The remainder is now 0, which means we have found the GCD. The last divisor used (9) is the GCD of 315 and 108.
Therefore, the greatest possible length of each tile that can cover the floor evenly is 9 inches.