A piece of paper is 280 millimeters long and 200 millimeters wide. You want to draw a grid on the paper so that there is a whole number of squares on the paper. What are the possible sizes of thet is the largest possible squares?

40

48

uuw

40

4,10
5,8

To find the largest possible squares that can fit on the given piece of paper, we need to determine the greatest common divisor (GCD) of the length and width. This is because the GCD represents the maximum size of the squares that can evenly fit into the given dimensions.

To find the GCD of 280 and 200, we can use various methods such as the Euclidean algorithm or prime factorization. Let's use the Euclidean algorithm:

Step 1: Divide the larger number (280) by the smaller number (200).
280 ÷ 200 = 1 remainder 80

Step 2: Next, divide the previous divisor (200) by the remainder (80).
200 ÷ 80 = 2 remainder 40

Step 3: Repeat the process with the previous divisor (80) and the new remainder (40).
80 ÷ 40 = 2 remainder 0

Since we have reached a remainder of 0, our last divisor (40) is the GCD of 280 and 200.

Therefore, the GCD of 280 and 200 is 40. This means that the largest possible square that can fit evenly in both dimensions is 40 millimeters by 40 millimeters.

In addition to this square, you can also draw smaller squares with sides that are factors of 40, such as 20x20, 10x10, and so on.