What is the Greatest Common Factor of 2123 and 2128?

Greatest common factor (GCF) of 2123 and 2128 is 1.

GCF(2123,2128) = 1

We will now calculate the prime factors of 2123 and 2128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2123 and 2128.

How to find the GCF of 2123 and 2128?

We will first find the prime factorization of 2123 and 2128. After we will calculate the factors of 2123 and 2128 and find the biggest common factor number .

Step-1: Prime Factorization of 2123

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

2123 = 11¹ × 193¹

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 2123

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

1, 11, 193

Step-4: Factors of 2128

List of positive integer factors of 2128 that divides 2123 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 2123 and 2128. The biggest common factor number is the GCF number.
So the greatest common factor 2123 and 2128 is 1.

Also check out the Least Common Multiple of 2123 and 2128