What is the Greatest Common Factor of 16382 and 16400?

Greatest common factor (GCF) of 16382 and 16400 is 2.

GCF(16382,16400) = 2

We will now calculate the prime factors of 16382 and 16400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16382 and 16400.

How to find the GCF of 16382 and 16400?

We will first find the prime factorization of 16382 and 16400. After we will calculate the factors of 16382 and 16400 and find the biggest common factor number .

Step-1: Prime Factorization of 16382

Prime factors of 16382 are 2, 8191. Prime factorization of 16382 in exponential form is:

16382 = 2¹ × 8191¹

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 16382

List of positive integer factors of 16382 that divides 16382 without a remainder.

1, 2, 8191

Step-4: Factors of 16400

List of positive integer factors of 16400 that divides 16382 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 16382 and 16400. The biggest common factor number is the GCF number.
So the greatest common factor 16382 and 16400 is 2.

Also check out the Least Common Multiple of 16382 and 16400