What is the Greatest Common Factor of 12132 and 12144?

Greatest common factor (GCF) of 12132 and 12144 is 12.

GCF(12132,12144) = 12

We will now calculate the prime factors of 12132 and 12144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12132 and 12144.

How to find the GCF of 12132 and 12144?

We will first find the prime factorization of 12132 and 12144. After we will calculate the factors of 12132 and 12144 and find the biggest common factor number .

Step-1: Prime Factorization of 12132

Prime factors of 12132 are 2, 3, 337. Prime factorization of 12132 in exponential form is:

12132 = 2² × 3² × 337¹

Step-2: Prime Factorization of 12144

Prime factors of 12144 are 2, 3, 11, 23. Prime factorization of 12144 in exponential form is:

12144 = 2⁴ × 3¹ × 11¹ × 23¹

Step-3: Factors of 12132

List of positive integer factors of 12132 that divides 12132 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 337, 674, 1011, 1348, 2022, 3033, 4044, 6066

Step-4: Factors of 12144

List of positive integer factors of 12144 that divides 12132 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 33, 44, 46, 48, 66, 69, 88, 92, 132, 138, 176, 184, 253, 264, 276, 368, 506, 528, 552, 759, 1012, 1104, 1518, 2024, 3036, 4048, 6072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12132 and 12144. The biggest common factor number is the GCF number.
So the greatest common factor 12132 and 12144 is 12.

Also check out the Least Common Multiple of 12132 and 12144