What is the Greatest Common Factor of 2109 and 2124?

Greatest common factor (GCF) of 2109 and 2124 is 3.

GCF(2109,2124) = 3

We will now calculate the prime factors of 2109 and 2124, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2124.

How to find the GCF of 2109 and 2124?

We will first find the prime factorization of 2109 and 2124. After we will calculate the factors of 2109 and 2124 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 2124

Prime factors of 2124 are 2, 3, 59. Prime factorization of 2124 in exponential form is:

2124 = 2² × 3² × 59¹

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 2124

List of positive integer factors of 2124 that divides 2109 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 59, 118, 177, 236, 354, 531, 708, 1062

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2124. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2124 is 3.

Also check out the Least Common Multiple of 2109 and 2124