What is the Greatest Common Factor of 18144 and 18164?

Greatest common factor (GCF) of 18144 and 18164 is 4.

GCF(18144,18164) = 4

We will now calculate the prime factors of 18144 and 18164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18144 and 18164.

How to find the GCF of 18144 and 18164?

We will first find the prime factorization of 18144 and 18164. After we will calculate the factors of 18144 and 18164 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 18164

Prime factors of 18164 are 2, 19, 239. Prime factorization of 18164 in exponential form is:

18164 = 2² × 19¹ × 239¹

Step-3: Factors of 18144

List of positive integer factors of 18144 that divides 18144 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

Step-4: Factors of 18164

List of positive integer factors of 18164 that divides 18144 without a remainder.

1, 2, 4, 19, 38, 76, 239, 478, 956, 4541, 9082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18144 and 18164. The biggest common factor number is the GCF number.
So the greatest common factor 18144 and 18164 is 4.

Also check out the Least Common Multiple of 18144 and 18164