A floor is 45 inches by 30 iinches. what is the largest square tile you could use to cover the floor?
15"
To determine the largest square tile that can cover the floor, we need to find the greatest common divisor (GCD) of the floor's dimensions, which will give us the length of the square tile's side.
Step 1: Find the GCD of 45 and 30 (the dimensions of the floor).
To find the GCD, you can use various methods such as prime factorization, Euclidean algorithm, or using a calculator with a GCD function.
Using the Euclidean algorithm:
- Divide the larger number (45) by the smaller number (30): 45 ÷ 30 = 1 remainder 15.
- Next, divide the divisor (30) by the remainder (15): 30 ÷ 15 = 2 with no remainder.
- Since we obtained a remainder of 0, the last divisor (15) is the GCD of 45 and 30.
Therefore, the GCD of 45 and 30 is 15.
Step 2: Determine the largest square tile size.
The side length of the largest square tile that can cover the floor is equal to the GCD obtained in Step 1, which is 15 inches.
Hence, the largest square tile you could use to cover the floor is a 15-inch by 15-inch tile.