What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

Options

A. 840
B. 841
C. 820
D. 814

Answer

To find the least number of square tiles required to pave the floor of a room that is 15 m 17 cm long and 9 m 2 cm broad, we can follow these steps:

### Step 1: Convert the dimensions to centimeters
1. **Convert the length**:
- 15 m = 15 × 100 cm = 1500 cm
- 17 cm remains as 17 cm
- Total length = 1500 cm + 17 cm = **1517 cm**

2. **Convert the width**:
- 9 m = 9 × 100 cm = 900 cm
- 2 cm remains as 2 cm
- Total width = 900 cm + 2 cm = **902 cm**

### Step 2: Find the area of the room
- Area = Length × Width
- Area = 1517 cm × 902 cm
- Area = **1,368,534 cm²**

### Step 3: Find the highest common factor (HCF) of the dimensions
1. **Factor the length (1517)**:
- 1517 = 37 × 41 (as determined from the video)

2. **Factor the width (902)**:
- 902 = 2 × 41 × 11 (as determined from the video)

3. **Find the HCF**:
- The common factor between 1517 and 902 is **41 cm**.

### Step 4: Calculate the area of one square tile
- Area of one square tile = side × side = 41 cm × 41 cm = **1681 cm²**.

### Step 5: Calculate the number of tiles required
- Number of tiles = Total area of the room / Area of one tile
- Number of tiles = 1,368,534 cm² / 1681 cm²
- Number of tiles = **814**.

### Final Answer
The least number of square tiles required to pave the floor of the room is **814 tiles**.

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