What is the Greatest Common Factor of 12072 and 12084?

Greatest common factor (GCF) of 12072 and 12084 is 12.

GCF(12072,12084) = 12

We will now calculate the prime factors of 12072 and 12084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12072 and 12084.

How to find the GCF of 12072 and 12084?

We will first find the prime factorization of 12072 and 12084. After we will calculate the factors of 12072 and 12084 and find the biggest common factor number .

Step-1: Prime Factorization of 12072

Prime factors of 12072 are 2, 3, 503. Prime factorization of 12072 in exponential form is:

12072 = 2³ × 3¹ × 503¹

Step-2: Prime Factorization of 12084

Prime factors of 12084 are 2, 3, 19, 53. Prime factorization of 12084 in exponential form is:

12084 = 2² × 3¹ × 19¹ × 53¹

Step-3: Factors of 12072

List of positive integer factors of 12072 that divides 12072 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 503, 1006, 1509, 2012, 3018, 4024, 6036

Step-4: Factors of 12084

List of positive integer factors of 12084 that divides 12072 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 53, 57, 76, 106, 114, 159, 212, 228, 318, 636, 1007, 2014, 3021, 4028, 6042

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12072 and 12084. The biggest common factor number is the GCF number.
So the greatest common factor 12072 and 12084 is 12.

Also check out the Least Common Multiple of 12072 and 12084