What is the Greatest Common Factor of 38384 and 38400?

Greatest common factor (GCF) of 38384 and 38400 is 16.

GCF(38384,38400) = 16

We will now calculate the prime factors of 38384 and 38400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38384 and 38400.

How to find the GCF of 38384 and 38400?

We will first find the prime factorization of 38384 and 38400. After we will calculate the factors of 38384 and 38400 and find the biggest common factor number .

Step-1: Prime Factorization of 38384

Prime factors of 38384 are 2, 2399. Prime factorization of 38384 in exponential form is:

38384 = 2⁴ × 2399¹

Step-2: 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-3: Factors of 38384

List of positive integer factors of 38384 that divides 38384 without a remainder.

1, 2, 4, 8, 16, 2399, 4798, 9596, 19192

Step-4: Factors of 38400

List of positive integer factors of 38400 that divides 38384 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38384 and 38400. The biggest common factor number is the GCF number.
So the greatest common factor 38384 and 38400 is 16.

Also check out the Least Common Multiple of 38384 and 38400