What is the Greatest Common Factor of 2109 and 2128?

Greatest common factor (GCF) of 2109 and 2128 is 19.

GCF(2109,2128) = 19

We will now calculate the prime factors of 2109 and 2128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2109 and 2128.

How to find the GCF of 2109 and 2128?

We will first find the prime factorization of 2109 and 2128. After we will calculate the factors of 2109 and 2128 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 2128

Prime factors of 2128 are 2, 7, 19. Prime factorization of 2128 in exponential form is:

2128 = 2⁴ × 7¹ × 19¹

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 2128

List of positive integer factors of 2128 that divides 2109 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2109 and 2128. The biggest common factor number is the GCF number.
So the greatest common factor 2109 and 2128 is 19.

Also check out the Least Common Multiple of 2109 and 2128