What is the Greatest Common Factor of 12084 and 12100?

Greatest common factor (GCF) of 12084 and 12100 is 4.

GCF(12084,12100) = 4

We will now calculate the prime factors of 12084 and 12100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12084 and 12100.

How to find the GCF of 12084 and 12100?

We will first find the prime factorization of 12084 and 12100. After we will calculate the factors of 12084 and 12100 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12100

Prime factors of 12100 are 2, 5, 11. Prime factorization of 12100 in exponential form is:

12100 = 2² × 5² × 11²

Step-3: Factors of 12084

List of positive integer factors of 12084 that divides 12084 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

Step-4: Factors of 12100

List of positive integer factors of 12100 that divides 12084 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12084 and 12100. The biggest common factor number is the GCF number.
So the greatest common factor 12084 and 12100 is 4.

Also check out the Least Common Multiple of 12084 and 12100