What is the Greatest Common Factor of 2034 and 2038?

Greatest common factor (GCF) of 2034 and 2038 is 2.

GCF(2034,2038) = 2

We will now calculate the prime factors of 2034 and 2038, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2034 and 2038.

How to find the GCF of 2034 and 2038?

We will first find the prime factorization of 2034 and 2038. After we will calculate the factors of 2034 and 2038 and find the biggest common factor number .

Step-1: Prime Factorization of 2034

Prime factors of 2034 are 2, 3, 113. Prime factorization of 2034 in exponential form is:

2034 = 2¹ × 3² × 113¹

Step-2: Prime Factorization of 2038

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

2038 = 2¹ × 1019¹

Step-3: Factors of 2034

List of positive integer factors of 2034 that divides 2034 without a remainder.

1, 2, 3, 6, 9, 18, 113, 226, 339, 678, 1017

Step-4: Factors of 2038

List of positive integer factors of 2038 that divides 2034 without a remainder.

1, 2, 1019

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2034 and 2038. The biggest common factor number is the GCF number.
So the greatest common factor 2034 and 2038 is 2.

Also check out the Least Common Multiple of 2034 and 2038