What is the Greatest Common Factor of 38400 and 38405?

Greatest common factor (GCF) of 38400 and 38405 is 5.

GCF(38400,38405) = 5

We will now calculate the prime factors of 38400 and 38405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38400 and 38405.

How to find the GCF of 38400 and 38405?

We will first find the prime factorization of 38400 and 38405. After we will calculate the factors of 38400 and 38405 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 38405

Prime factors of 38405 are 5, 7681. Prime factorization of 38405 in exponential form is:

38405 = 5¹ × 7681¹

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 38405

List of positive integer factors of 38405 that divides 38400 without a remainder.

1, 5, 7681

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38400 and 38405. The biggest common factor number is the GCF number.
So the greatest common factor 38400 and 38405 is 5.

Also check out the Least Common Multiple of 38400 and 38405