What is the Greatest Common Factor of 2119 and 2128?

Greatest common factor (GCF) of 2119 and 2128 is 1.

GCF(2119,2128) = 1

We will now calculate the prime factors of 2119 and 2128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2119 and 2128.

How to find the GCF of 2119 and 2128?

We will first find the prime factorization of 2119 and 2128. After we will calculate the factors of 2119 and 2128 and find the biggest common factor number .

Step-1: Prime Factorization of 2119

Prime factors of 2119 are 13, 163. Prime factorization of 2119 in exponential form is:

2119 = 13¹ × 163¹

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 2119

List of positive integer factors of 2119 that divides 2119 without a remainder.

1, 13, 163

Step-4: Factors of 2128

List of positive integer factors of 2128 that divides 2119 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 2119 and 2128. The biggest common factor number is the GCF number.
So the greatest common factor 2119 and 2128 is 1.

Also check out the Least Common Multiple of 2119 and 2128