What is the Greatest Common Factor of 2180 and 2198?

Greatest common factor (GCF) of 2180 and 2198 is 2.

GCF(2180,2198) = 2

We will now calculate the prime factors of 2180 and 2198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2180 and 2198.

How to find the GCF of 2180 and 2198?

We will first find the prime factorization of 2180 and 2198. After we will calculate the factors of 2180 and 2198 and find the biggest common factor number .

Step-1: Prime Factorization of 2180

Prime factors of 2180 are 2, 5, 109. Prime factorization of 2180 in exponential form is:

2180 = 2² × 5¹ × 109¹

Step-2: 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-3: Factors of 2180

List of positive integer factors of 2180 that divides 2180 without a remainder.

1, 2, 4, 5, 10, 20, 109, 218, 436, 545, 1090

Step-4: Factors of 2198

List of positive integer factors of 2198 that divides 2180 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2180 and 2198. The biggest common factor number is the GCF number.
So the greatest common factor 2180 and 2198 is 2.

Also check out the Least Common Multiple of 2180 and 2198