What is the Greatest Common Factor of 18129 and 18144?

Greatest common factor (GCF) of 18129 and 18144 is 3.

GCF(18129,18144) = 3

We will now calculate the prime factors of 18129 and 18144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18129 and 18144.

How to find the GCF of 18129 and 18144?

We will first find the prime factorization of 18129 and 18144. After we will calculate the factors of 18129 and 18144 and find the biggest common factor number .

Step-1: Prime Factorization of 18129

Prime factors of 18129 are 3, 6043. Prime factorization of 18129 in exponential form is:

18129 = 3¹ × 6043¹

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 18129

List of positive integer factors of 18129 that divides 18129 without a remainder.

1, 3, 6043

Step-4: Factors of 18144

List of positive integer factors of 18144 that divides 18129 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 18129 and 18144. The biggest common factor number is the GCF number.
So the greatest common factor 18129 and 18144 is 3.

Also check out the Least Common Multiple of 18129 and 18144