What is the Greatest Common Factor of 38400 and 38406?

Greatest common factor (GCF) of 38400 and 38406 is 6.

GCF(38400,38406) = 6

We will now calculate the prime factors of 38400 and 38406, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38400 and 38406.

How to find the GCF of 38400 and 38406?

We will first find the prime factorization of 38400 and 38406. After we will calculate the factors of 38400 and 38406 and find the biggest common factor number .

Step-1: Prime Factorization of 38400

Prime factors of 38400 are 2, 3, 5. Prime factorization of 38400 in exponential form is:

38400 = 2⁹ × 3¹ × 5²

Step-2: Prime Factorization of 38406

Prime factors of 38406 are 2, 3, 37, 173. Prime factorization of 38406 in exponential form is:

38406 = 2¹ × 3¹ × 37¹ × 173¹

Step-3: Factors of 38400

List of positive integer factors of 38400 that divides 38400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3200, 3840, 4800, 6400, 7680, 9600, 12800, 19200

Step-4: Factors of 38406

List of positive integer factors of 38406 that divides 38400 without a remainder.

1, 2, 3, 6, 37, 74, 111, 173, 222, 346, 519, 1038, 6401, 12802, 19203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38400 and 38406. The biggest common factor number is the GCF number.
So the greatest common factor 38400 and 38406 is 6.

Also check out the Least Common Multiple of 38400 and 38406