What is the Greatest Common Factor of 2178 and 2189?

Greatest common factor (GCF) of 2178 and 2189 is 11.

GCF(2178,2189) = 11

We will now calculate the prime factors of 2178 and 2189, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2178 and 2189.

How to find the GCF of 2178 and 2189?

We will first find the prime factorization of 2178 and 2189. After we will calculate the factors of 2178 and 2189 and find the biggest common factor number .

Step-1: Prime Factorization of 2178

Prime factors of 2178 are 2, 3, 11. Prime factorization of 2178 in exponential form is:

2178 = 2¹ × 3² × 11²

Step-2: Prime Factorization of 2189

Prime factors of 2189 are 11, 199. Prime factorization of 2189 in exponential form is:

2189 = 11¹ × 199¹

Step-3: Factors of 2178

List of positive integer factors of 2178 that divides 2178 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089

Step-4: Factors of 2189

List of positive integer factors of 2189 that divides 2178 without a remainder.

1, 11, 199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2178 and 2189. The biggest common factor number is the GCF number.
So the greatest common factor 2178 and 2189 is 11.

Also check out the Least Common Multiple of 2178 and 2189