What is the Greatest Common Factor of 38912 and 38920?

Greatest common factor (GCF) of 38912 and 38920 is 8.

GCF(38912,38920) = 8

We will now calculate the prime factors of 38912 and 38920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38912 and 38920.

How to find the GCF of 38912 and 38920?

We will first find the prime factorization of 38912 and 38920. After we will calculate the factors of 38912 and 38920 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 38920

Prime factors of 38920 are 2, 5, 7, 139. Prime factorization of 38920 in exponential form is:

38920 = 2³ × 5¹ × 7¹ × 139¹

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 38920

List of positive integer factors of 38920 that divides 38912 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 139, 140, 278, 280, 556, 695, 973, 1112, 1390, 1946, 2780, 3892, 4865, 5560, 7784, 9730, 19460

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38912 and 38920. The biggest common factor number is the GCF number.
So the greatest common factor 38912 and 38920 is 8.

Also check out the Least Common Multiple of 38912 and 38920