What is the Greatest Common Factor of 38912 and 38916?

Greatest common factor (GCF) of 38912 and 38916 is 4.

GCF(38912,38916) = 4

We will now calculate the prime factors of 38912 and 38916, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38912 and 38916.

How to find the GCF of 38912 and 38916?

We will first find the prime factorization of 38912 and 38916. After we will calculate the factors of 38912 and 38916 and find the biggest common factor number .

Step-1: Prime Factorization of 38912

Prime factors of 38912 are 2, 19. Prime factorization of 38912 in exponential form is:

38912 = 2¹¹ × 19¹

Step-2: Prime Factorization of 38916

Prime factors of 38916 are 2, 3, 23, 47. Prime factorization of 38916 in exponential form is:

38916 = 2² × 3² × 23¹ × 47¹

Step-3: Factors of 38912

List of positive integer factors of 38912 that divides 38912 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1024, 1216, 2048, 2432, 4864, 9728, 19456

Step-4: Factors of 38916

List of positive integer factors of 38916 that divides 38912 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 47, 69, 92, 94, 138, 141, 188, 207, 276, 282, 414, 423, 564, 828, 846, 1081, 1692, 2162, 3243, 4324, 6486, 9729, 12972, 19458

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38912 and 38916. The biggest common factor number is the GCF number.
So the greatest common factor 38912 and 38916 is 4.

Also check out the Least Common Multiple of 38912 and 38916