Question

what is the side length in inches of the largest square tile that can tile a 6 - inch by 9 - inch rectangle completely? what is the side length in inches of the smallest square that can be created with 6 - inch by 9 - inch rectangular tiles?

Explanation:

Step1: Find the GCD of 6 and 9

We need to find the greatest - common divisor (GCD) of the two side - lengths of the rectangle (6 and 9) to get the side - length of the largest square tile. Prime factorize 6 and 9. $6 = 2\times3$ and $9=3\times3$. The common factor is 3.

Step2: Determine the side - length

The GCD of 6 and 9 is 3. So the side - length of the largest square tile that can tile a 6 - inch by 9 - inch rectangle completely is 3 inches.

Answer:

3 inches