What is the Greatest Common Factor of 2109 and 2114?

Greatest common factor (GCF) of 2109 and 2114 is 1.

GCF(2109,2114) = 1

We will now calculate the prime factors of 2109 and 2114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2114.

How to find the GCF of 2109 and 2114?

We will first find the prime factorization of 2109 and 2114. After we will calculate the factors of 2109 and 2114 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 2114

Prime factors of 2114 are 2, 7, 151. Prime factorization of 2114 in exponential form is:

2114 = 2¹ × 7¹ × 151¹

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 2114

List of positive integer factors of 2114 that divides 2109 without a remainder.

1, 2, 7, 14, 151, 302, 1057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2114. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2114 is 1.

Also check out the Least Common Multiple of 2109 and 2114