What is the Greatest Common Factor of 2198 and 2209?

Greatest common factor (GCF) of 2198 and 2209 is 1.

GCF(2198,2209) = 1

We will now calculate the prime factors of 2198 and 2209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2198 and 2209.

How to find the GCF of 2198 and 2209?

We will first find the prime factorization of 2198 and 2209. After we will calculate the factors of 2198 and 2209 and find the biggest common factor number .

Step-1: Prime Factorization of 2198

Prime factors of 2198 are 2, 7, 157. Prime factorization of 2198 in exponential form is:

2198 = 2¹ × 7¹ × 157¹

Step-2: Prime Factorization of 2209

Prime factors of 2209 are 47. Prime factorization of 2209 in exponential form is:

2209 = 47²

Step-3: Factors of 2198

List of positive integer factors of 2198 that divides 2198 without a remainder.

1, 2, 7, 14, 157, 314, 1099

Step-4: Factors of 2209

List of positive integer factors of 2209 that divides 2198 without a remainder.

1, 47

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2198 and 2209. The biggest common factor number is the GCF number.
So the greatest common factor 2198 and 2209 is 1.

Also check out the Least Common Multiple of 2198 and 2209