What is the Greatest Common Factor of 18132 and 18144?

Greatest common factor (GCF) of 18132 and 18144 is 12.

GCF(18132,18144) = 12

We will now calculate the prime factors of 18132 and 18144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18132 and 18144.

How to find the GCF of 18132 and 18144?

We will first find the prime factorization of 18132 and 18144. After we will calculate the factors of 18132 and 18144 and find the biggest common factor number .

Step-1: Prime Factorization of 18132

Prime factors of 18132 are 2, 3, 1511. Prime factorization of 18132 in exponential form is:

18132 = 2² × 3¹ × 1511¹

Step-2: Prime Factorization of 18144

Prime factors of 18144 are 2, 3, 7. Prime factorization of 18144 in exponential form is:

18144 = 2⁵ × 3⁴ × 7¹

Step-3: Factors of 18132

List of positive integer factors of 18132 that divides 18132 without a remainder.

1, 2, 3, 4, 6, 12, 1511, 3022, 4533, 6044, 9066

Step-4: Factors of 18144

List of positive integer factors of 18144 that divides 18132 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 81, 84, 96, 108, 112, 126, 144, 162, 168, 189, 216, 224, 252, 288, 324, 336, 378, 432, 504, 567, 648, 672, 756, 864, 1008, 1134, 1296, 1512, 2016, 2268, 2592, 3024, 4536, 6048, 9072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18132 and 18144. The biggest common factor number is the GCF number.
So the greatest common factor 18132 and 18144 is 12.

Also check out the Least Common Multiple of 18132 and 18144