What is the Greatest Common Factor of 2109 and 2117?

Greatest common factor (GCF) of 2109 and 2117 is 1.

GCF(2109,2117) = 1

We will now calculate the prime factors of 2109 and 2117, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2117.

How to find the GCF of 2109 and 2117?

We will first find the prime factorization of 2109 and 2117. After we will calculate the factors of 2109 and 2117 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 2117

Prime factors of 2117 are 29, 73. Prime factorization of 2117 in exponential form is:

2117 = 29¹ × 73¹

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 2117

List of positive integer factors of 2117 that divides 2109 without a remainder.

1, 29, 73

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2117. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2117 is 1.

Also check out the Least Common Multiple of 2109 and 2117