What is the Greatest Common Factor of 2034 and 2052?

Greatest common factor (GCF) of 2034 and 2052 is 18.

GCF(2034,2052) = 18

We will now calculate the prime factors of 2034 and 2052, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2034 and 2052.

How to find the GCF of 2034 and 2052?

We will first find the prime factorization of 2034 and 2052. After we will calculate the factors of 2034 and 2052 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 2052

Prime factors of 2052 are 2, 3, 19. Prime factorization of 2052 in exponential form is:

2052 = 2² × 3³ × 19¹

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 2052

List of positive integer factors of 2052 that divides 2034 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 27, 36, 38, 54, 57, 76, 108, 114, 171, 228, 342, 513, 684, 1026

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2034 and 2052. The biggest common factor number is the GCF number.
So the greatest common factor 2034 and 2052 is 18.

Also check out the Least Common Multiple of 2034 and 2052