What is the Greatest Common Factor of 6075 and 6084?

Greatest common factor (GCF) of 6075 and 6084 is 9.

GCF(6075,6084) = 9

We will now calculate the prime factors of 6075 and 6084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6075 and 6084.

How to find the GCF of 6075 and 6084?

We will first find the prime factorization of 6075 and 6084. After we will calculate the factors of 6075 and 6084 and find the biggest common factor number .

Step-1: Prime Factorization of 6075

Prime factors of 6075 are 3, 5. Prime factorization of 6075 in exponential form is:

6075 = 3⁵ × 5²

Step-2: Prime Factorization of 6084

Prime factors of 6084 are 2, 3, 13. Prime factorization of 6084 in exponential form is:

6084 = 2² × 3² × 13²

Step-3: Factors of 6075

List of positive integer factors of 6075 that divides 6075 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 243, 405, 675, 1215, 2025

Step-4: Factors of 6084

List of positive integer factors of 6084 that divides 6075 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 169, 234, 338, 468, 507, 676, 1014, 1521, 2028, 3042

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6075 and 6084. The biggest common factor number is the GCF number.
So the greatest common factor 6075 and 6084 is 9.

Also check out the Least Common Multiple of 6075 and 6084