What is the Greatest Common Factor of 2109 and 2123?

Greatest common factor (GCF) of 2109 and 2123 is 1.

GCF(2109,2123) = 1

We will now calculate the prime factors of 2109 and 2123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2123.

How to find the GCF of 2109 and 2123?

We will first find the prime factorization of 2109 and 2123. After we will calculate the factors of 2109 and 2123 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 2123

Prime factors of 2123 are 11, 193. Prime factorization of 2123 in exponential form is:

2123 = 11¹ × 193¹

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 2123

List of positive integer factors of 2123 that divides 2109 without a remainder.

1, 11, 193

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2123. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2123 is 1.

Also check out the Least Common Multiple of 2109 and 2123