What is the Greatest Common Factor of 200 and 209?

Greatest common factor (GCF) of 200 and 209 is 1.

GCF(200,209) = 1

We will now calculate the prime factors of 200 and 209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 209.

How to find the GCF of 200 and 209?

We will first find the prime factorization of 200 and 209. After we will calculate the factors of 200 and 209 and find the biggest common factor number .

Step-1: Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 5²

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 200

List of positive integer factors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Step-4: Factors of 209

List of positive integer factors of 209 that divides 200 without a remainder.

1, 11, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 209. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 209 is 1.

Also check out the Least Common Multiple of 200 and 209