What is the Greatest Common Factor of 190 and 209?

Greatest common factor (GCF) of 190 and 209 is 19.

GCF(190,209) = 19

We will now calculate the prime factors of 190 and 209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 190 and 209.

How to find the GCF of 190 and 209?

We will first find the prime factorization of 190 and 209. After we will calculate the factors of 190 and 209 and find the biggest common factor number .

Step-1: Prime Factorization of 190

Prime factors of 190 are 2, 5, 19. Prime factorization of 190 in exponential form is:

190 = 2¹ × 5¹ × 19¹

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 190

List of positive integer factors of 190 that divides 190 without a remainder.

1, 2, 5, 10, 19, 38, 95

Step-4: Factors of 209

List of positive integer factors of 209 that divides 190 without a remainder.

1, 11, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 190 and 209. The biggest common factor number is the GCF number.
So the greatest common factor 190 and 209 is 19.

Also check out the Least Common Multiple of 190 and 209