Two distinct natural numbers x and y are such that, x + y = 2250. What is the maximum possible HCF?

The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder.

In this case, we are given that x + y = 2250 and x and y are distinct natural numbers.

The maximum possible HCF for two numbers is achieved when the two numbers are equal. However, since x and y are distinct, they cannot be equal.

Therefore, the maximum possible HCF is achieved when one number is as small as possible and the other is as large as possible.

The smallest possible value for one of the numbers (let's say x) is 1 (since they are natural numbers). This makes the other number (y) equal to 2250 - 1 = 2249.

Therefore, the maximum possible HCF of x and y is 1.