What is the Greatest Common Factor of 198 and 209?

Greatest common factor (GCF) of 198 and 209 is 11.

GCF(198,209) = 11

We will now calculate the prime factors of 198 and 209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 198 and 209.

How to find the GCF of 198 and 209?

We will first find the prime factorization of 198 and 209. After we will calculate the factors of 198 and 209 and find the biggest common factor number .

Step-1: Prime Factorization of 198

Prime factors of 198 are 2, 3, 11. Prime factorization of 198 in exponential form is:

198 = 2¹ × 3² × 11¹

Step-2: Prime Factorization of 209

Prime factors of 209 are 11, 19. Prime factorization of 209 in exponential form is:

209 = 11¹ × 19¹

Step-3: Factors of 198

List of positive integer factors of 198 that divides 198 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99

Step-4: Factors of 209

List of positive integer factors of 209 that divides 198 without a remainder.

1, 11, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 198 and 209. The biggest common factor number is the GCF number.
So the greatest common factor 198 and 209 is 11.

Also check out the Least Common Multiple of 198 and 209