What is the Greatest Common Factor of 209 and 218?

Greatest common factor (GCF) of 209 and 218 is 1.

GCF(209,218) = 1

We will now calculate the prime factors of 209 and 218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 209 and 218.

How to find the GCF of 209 and 218?

We will first find the prime factorization of 209 and 218. After we will calculate the factors of 209 and 218 and find the biggest common factor number .

Step-1: Prime Factorization of 209

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

209 = 11¹ × 19¹

Step-2: Prime Factorization of 218

Prime factors of 218 are 2, 109. Prime factorization of 218 in exponential form is:

218 = 2¹ × 109¹

Step-3: Factors of 209

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

1, 11, 19

Step-4: Factors of 218

List of positive integer factors of 218 that divides 209 without a remainder.

1, 2, 109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 209 and 218. The biggest common factor number is the GCF number.
So the greatest common factor 209 and 218 is 1.

Also check out the Least Common Multiple of 209 and 218