What is the Greatest Common Factor of 16384 and 16400?

Greatest common factor (GCF) of 16384 and 16400 is 16.

GCF(16384,16400) = 16

We will now calculate the prime factors of 16384 and 16400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16384 and 16400.

How to find the GCF of 16384 and 16400?

We will first find the prime factorization of 16384 and 16400. After we will calculate the factors of 16384 and 16400 and find the biggest common factor number .

Step-1: Prime Factorization of 16384

Prime factors of 16384 are 2. Prime factorization of 16384 in exponential form is:

16384 = 2¹⁴

Step-2: Prime Factorization of 16400

Prime factors of 16400 are 2, 5, 41. Prime factorization of 16400 in exponential form is:

16400 = 2⁴ × 5² × 41¹

Step-3: Factors of 16384

List of positive integer factors of 16384 that divides 16384 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Step-4: Factors of 16400

List of positive integer factors of 16400 that divides 16384 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 164, 200, 205, 328, 400, 410, 656, 820, 1025, 1640, 2050, 3280, 4100, 8200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16384 and 16400. The biggest common factor number is the GCF number.
So the greatest common factor 16384 and 16400 is 16.

Also check out the Least Common Multiple of 16384 and 16400