What is the Greatest Common Factor of 2109 and 2129?

Greatest common factor (GCF) of 2109 and 2129 is 1.

GCF(2109,2129) = 1

We will now calculate the prime factors of 2109 and 2129, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2129.

How to find the GCF of 2109 and 2129?

We will first find the prime factorization of 2109 and 2129. After we will calculate the factors of 2109 and 2129 and find the biggest common factor number .

Step-1: Prime Factorization of 2109

Prime factors of 2109 are 3, 19, 37. Prime factorization of 2109 in exponential form is:

2109 = 3¹ × 19¹ × 37¹

Step-2: Prime Factorization of 2129

Prime factors of 2129 are 2129. Prime factorization of 2129 in exponential form is:

2129 = 2129¹

Step-3: Factors of 2109

List of positive integer factors of 2109 that divides 2109 without a remainder.

1, 3, 19, 37, 57, 111, 703

Step-4: Factors of 2129

List of positive integer factors of 2129 that divides 2109 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2129. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2129 is 1.

Also check out the Least Common Multiple of 2109 and 2129