What is the Greatest Common Factor of 36864 and 36874?

Greatest common factor (GCF) of 36864 and 36874 is 2.

GCF(36864,36874) = 2

We will now calculate the prime factors of 36864 and 36874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36864 and 36874.

How to find the GCF of 36864 and 36874?

We will first find the prime factorization of 36864 and 36874. After we will calculate the factors of 36864 and 36874 and find the biggest common factor number .

Step-1: Prime Factorization of 36864

Prime factors of 36864 are 2, 3. Prime factorization of 36864 in exponential form is:

36864 = 2¹² × 3²

Step-2: Prime Factorization of 36874

Prime factors of 36874 are 2, 103, 179. Prime factorization of 36874 in exponential form is:

36874 = 2¹ × 103¹ × 179¹

Step-3: Factors of 36864

List of positive integer factors of 36864 that divides 36864 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2048, 2304, 3072, 4096, 4608, 6144, 9216, 12288, 18432

Step-4: Factors of 36874

List of positive integer factors of 36874 that divides 36864 without a remainder.

1, 2, 103, 179, 206, 358, 18437

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36864 and 36874. The biggest common factor number is the GCF number.
So the greatest common factor 36864 and 36874 is 2.

Also check out the Least Common Multiple of 36864 and 36874