What is the Greatest Common Factor of 2038 and 2054?

Greatest common factor (GCF) of 2038 and 2054 is 2.

GCF(2038,2054) = 2

We will now calculate the prime factors of 2038 and 2054, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2038 and 2054.

How to find the GCF of 2038 and 2054?

We will first find the prime factorization of 2038 and 2054. After we will calculate the factors of 2038 and 2054 and find the biggest common factor number .

Step-1: Prime Factorization of 2038

Prime factors of 2038 are 2, 1019. Prime factorization of 2038 in exponential form is:

2038 = 2¹ × 1019¹

Step-2: Prime Factorization of 2054

Prime factors of 2054 are 2, 13, 79. Prime factorization of 2054 in exponential form is:

2054 = 2¹ × 13¹ × 79¹

Step-3: Factors of 2038

List of positive integer factors of 2038 that divides 2038 without a remainder.

1, 2, 1019

Step-4: Factors of 2054

List of positive integer factors of 2054 that divides 2038 without a remainder.

1, 2, 13, 26, 79, 158, 1027

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2038 and 2054. The biggest common factor number is the GCF number.
So the greatest common factor 2038 and 2054 is 2.

Also check out the Least Common Multiple of 2038 and 2054