What is the largest size of square tiles that can be used to cover the floor of a room of size `5.25 m xx 4.55m?`

Options

A. 25cm
B. 35cm
C. 45cm
D. 55cm

Answer

To find the largest size of square tiles that can be used to cover a room of size 5.25 m by 4.55 m, we need to determine the greatest common divisor (GCD) of the two dimensions. Here’s a step-by-step solution:

### Step 1: Convert dimensions to the same unit
First, we convert the dimensions from meters to centimeters to avoid dealing with decimals.

- 5.25 m = 5.25 × 100 = 525 cm
- 4.55 m = 4.55 × 100 = 455 cm

**Hint:** Always convert measurements to the same unit for easier calculations.

### Step 2: Find the GCD of the two dimensions
Next, we need to find the GCD of 525 cm and 455 cm. We can do this using the prime factorization method or the Euclidean algorithm. Here, we'll use the prime factorization method.

**Prime Factorization of 525:**
- 525 = 5 × 105
- 105 = 5 × 21
- 21 = 3 × 7
- Therefore, 525 = 5² × 3 × 7

**Prime Factorization of 455:**
- 455 = 5 × 91
- 91 = 7 × 13
- Therefore, 455 = 5 × 7 × 13

**Hint:** Factor each number into its prime components to find common factors.

### Step 3: Identify common factors
Now, we identify the common prime factors from both factorizations:
- Common factors: 5 and 7

### Step 4: Calculate the GCD
To find the GCD, we take the product of the lowest powers of all common prime factors:
- GCD = 5¹ × 7¹ = 5 × 7 = 35

**Hint:** Multiply the common prime factors to get the GCD.

### Step 5: Conclusion
The largest size of square tiles that can be used to cover the floor of the room is 35 cm.

**Final Answer:** 35 cm