To find the greatest length of each squared marble that can evenly tile the entire rectangular floor, we'll need to find the largest possible square that fits into both the length and the breadth of the rectangle without leaving any gaps. This problem is best approached by finding the Greatest Common Divisor (GCD) of the length and the breadth of the rectangle.
Here are the steps to solve the problem:
1. Identify the dimensions of the rectangle:
- The length of the rectangle is 20 feet.
- The breadth of the rectangle is 16 feet.
2. Understand the concept of GCD:
- The Greatest Common Divisor (GCD) of two numbers is the largest number that can divide both of them without leaving a remainder. In this context, the GCD will represent the side length of the largest possible square tile that can completely cover the floor.
3. Calculate the GCD of 20 and 16:
- To find the GCD of 20 and 16, we'll consider the divisors of each:
- Divisors of 20: 1, 2, 4, 5, 10, 20
- Divisors of 16: 1, 2, 4, 8, 16
- The common divisors are 1, 2, and 4.
- The greatest of these common divisors is 4.
4. Conclusion:
- Therefore, the greatest length of each squared marble that can tile the rectangular floor is 4 feet.
Thus, the greatest length of each squared marble is 4 feet.
