What is the Greatest Common Factor of 2189 and 2200?

Greatest common factor (GCF) of 2189 and 2200 is 11.

GCF(2189,2200) = 11

We will now calculate the prime factors of 2189 and 2200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2189 and 2200.

How to find the GCF of 2189 and 2200?

We will first find the prime factorization of 2189 and 2200. After we will calculate the factors of 2189 and 2200 and find the biggest common factor number .

Step-1: Prime Factorization of 2189

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

2189 = 11¹ × 199¹

Step-2: Prime Factorization of 2200

Prime factors of 2200 are 2, 5, 11. Prime factorization of 2200 in exponential form is:

2200 = 2³ × 5² × 11¹

Step-3: Factors of 2189

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

1, 11, 199

Step-4: Factors of 2200

List of positive integer factors of 2200 that divides 2189 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2189 and 2200. The biggest common factor number is the GCF number.
So the greatest common factor 2189 and 2200 is 11.

Also check out the Least Common Multiple of 2189 and 2200