A room 16 m 5 cm long and 15m borad is to be fitted with equal square tiles. How many number of largest possible tiles are required so that they exactly fit ?

Options

A. 10400
B. 10700
C. 10800
D. 9800

Answer

To solve the problem of fitting the largest possible square tiles in a room that is 16 m 5 cm long and 15 m broad, we will follow these steps:

### Step 1: Convert Measurements to a Common Unit
Convert the dimensions of the room from meters and centimeters to centimeters for consistency.
- Length: 16 m 5 cm = 16 × 100 cm + 5 cm = 1600 cm + 5 cm = 1605 cm
- Width: 15 m = 15 × 100 cm = 1500 cm

### Step 2: Find the Greatest Common Factor (GCF)
To determine the size of the largest square tile that can fit perfectly, we need to find the GCF of the length and width of the room.
- Length (L) = 1605 cm
- Width (B) = 1500 cm

We will find the GCF of 1605 and 1500 using prime factorization or the Euclidean algorithm.

#### Prime Factorization:
- 1605 = 3 × 5 × 107
- 1500 = 2 × 2 × 3 × 5 × 5 × 3

The common factors are:
- 3 and 5

Thus, GCF = 3 × 5 = 15 cm.

### Step 3: Calculate the Area of Each Tile
Now that we have the side length of the largest square tile, we can calculate the area of one tile.
- Area of one tile = side × side = 15 cm × 15 cm = 225 cm².

### Step 4: Calculate the Area of the Room
Next, we calculate the area of the room.
- Area of the room = Length × Width = 1605 cm × 1500 cm = 2407500 cm².

### Step 5: Calculate the Number of Tiles Required
Finally, we can find out how many tiles are needed by dividing the area of the room by the area of one tile.
- Number of tiles = Area of the room / Area of one tile = 2407500 cm² / 225 cm².

Calculating this gives:
- Number of tiles = 2407500 / 225 = 10700 tiles.

### Final Answer
The number of largest possible square tiles required to fit the room is **10700 tiles**.

---