A rectangular courtyard is 57m 50 cm long and 22m broad.Determine the least possible number of square stones of the same size required to pave it.

Since 57 and 22 have no common factors, stones of 50cm will do the job.

In cm, the GCF(5750,2200) = 50

So, how many stones will that take?

5060

To determine the least possible number of square stones required to pave the rectangular courtyard, we need to find the greatest common divisor (GCD) of the length and breadth.

First, we need to convert the measurements to the same unit. Let's convert the length and breadth to centimeters:
- Length = 57m 50cm = (57 * 100) cm + 50 cm = 5750 cm
- Breadth = 22m = (22 * 100) cm = 2200 cm

Next, we can calculate the GCD of 5750 cm and 2200 cm to find the size of the square stones that can evenly divide both measurements.

The GCD can be found using the Euclidean algorithm:
Step 1: Divide 5750 cm by 2200 cm
5750 cm ÷ 2200 cm = 2 remainder 1350 cm
Step 2: Divide 2200 cm by 1350 cm
2200 cm ÷ 1350 cm = 1 remainder 850 cm
Step 3: Divide 1350 cm by 850 cm
1350 cm ÷ 850 cm = 1 remainder 500 cm
Step 4: Divide 850 cm by 500 cm
850 cm ÷ 500 cm = 1 remainder 350 cm
Step 5: Divide 500 cm by 350 cm
500 cm ÷ 350 cm = 1 remainder 150 cm
Step 6: Divide 350 cm by 150 cm
350 cm ÷ 150 cm = 2 remainder 50 cm
Step 7: Divide 150 cm by 50 cm
150 cm ÷ 50 cm = 3 remainder 0 cm

Since we have reached a remainder of 0 cm, the GCD is 50 cm.

Therefore, the least possible number of square stones of the same size required to pave the rectangular courtyard is determined by dividing the length and breadth by the GCD:
- Number of square stones along the length = 5750 cm ÷ 50 cm = 115
- Number of square stones along the breadth = 2200 cm ÷ 50 cm = 44

To cover the entire courtyard, we need to multiply these two numbers:
- Total number of square stones = 115 × 44 = 5060

Thus, a total of 5060 square stones of the same size are required to pave the rectangular courtyard.

To determine the least possible number of square stones required to pave the courtyard, we need to find the area of the courtyard in terms of the area of square stones.

To find the area of the courtyard, we multiply its length by its breadth:

Length = 57m 50cm = 57.50m
Breadth = 22m

Area of the courtyard = Length x Breadth

Area of the courtyard = 57.50m x 22m

Now, we have the area of the courtyard in square meters.

To find the area of a square stone, we need to know the size of each square stone. Let's assume each square stone has a side length of "x" meters.

The area of a square is given by the formula: Area = side length x side length

So, the area of each square stone is x meters x x meters = x^2 square meters.

Now, we need to find the least possible number of square stones required to cover the entire courtyard.

To determine this, we divide the area of the courtyard by the area of each square stone:

Number of square stones = Area of the courtyard / Area of each square stone

Number of square stones = (57.50m x 22m) / (x^2 square meters)

Once you determine the value of x (the side length of each square stone), you can proceed to calculate the number of square stones by plugging in the values into the equation.

Remember to convert the answer to the nearest whole number since we cannot have a fraction of a stone.