### Instruction: Find the greatest common divisor of 9,009 and 14,014.### Response: To find the greatest common divisor (GCD) of two numbers, I can use the Euclidean algorithm, which repeatedly applies the fact that GCD(a, b) = GCD(b, r), where r is the remainder when a is divided by b.
To apply the algorithm, I start by dividing the larger number by the smaller number and finding the remainder.
In this case, 14,014 / 9,009 = 1 with a remainder of 5,005.
This means that GCD(14,014, 9,009) = GCD(9,009, 5,005).
Next, I repeat the process with 9,009 and 5,005.
I get 9,009 / 5,005 = 1 with a remainder of 4,004.
This means that GCD(9,009, 5,005) = GCD(5,005, 4,004).
I keep going until I get a remainder of zero, which means that the last non-zero remainder is the GCD.
So I divide 5,005 by 4,004 and get 1 with a remainder of 1,001.
This means that GCD(5,005, 4,004) = GCD(4,004, 1,001).
Then I divide 4,004 by 1,001 and get 4 with a remainder of zero.