What is the Greatest Common Factor of 6129 and 6138?

Greatest common factor (GCF) of 6129 and 6138 is 9.

GCF(6129,6138) = 9

We will now calculate the prime factors of 6129 and 6138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6129 and 6138.

How to find the GCF of 6129 and 6138?

We will first find the prime factorization of 6129 and 6138. After we will calculate the factors of 6129 and 6138 and find the biggest common factor number .

Step-1: Prime Factorization of 6129

Prime factors of 6129 are 3, 227. Prime factorization of 6129 in exponential form is:

6129 = 3³ × 227¹

Step-2: Prime Factorization of 6138

Prime factors of 6138 are 2, 3, 11, 31. Prime factorization of 6138 in exponential form is:

6138 = 2¹ × 3² × 11¹ × 31¹

Step-3: Factors of 6129

List of positive integer factors of 6129 that divides 6129 without a remainder.

1, 3, 9, 27, 227, 681, 2043

Step-4: Factors of 6138

List of positive integer factors of 6138 that divides 6129 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 186, 198, 279, 341, 558, 682, 1023, 2046, 3069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6129 and 6138. The biggest common factor number is the GCF number.
So the greatest common factor 6129 and 6138 is 9.

Also check out the Least Common Multiple of 6129 and 6138