Find the greatest common divisor of 306 and 765.
The greatest common divisor of 306 and 765 is

Step 1 ：The problem is to find the greatest common divisor of 306 and 765.

Step 2 ：The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder.

Step 3 ：We can use the Euclidean algorithm to find the GCD of two numbers. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.

Step 4 ：By applying the Euclidean algorithm, we find that the greatest common divisor of 306 and 765 is 9.

Step 5 ：Final Answer: \(\boxed{9}\)