What is the Greatest Common Factor of 6400 and 6409?

Greatest common factor (GCF) of 6400 and 6409 is 1.

GCF(6400,6409) = 1

We will now calculate the prime factors of 6400 and 6409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6400 and 6409.

How to find the GCF of 6400 and 6409?

We will first find the prime factorization of 6400 and 6409. After we will calculate the factors of 6400 and 6409 and find the biggest common factor number .

Step-1: Prime Factorization of 6400

Prime factors of 6400 are 2, 5. Prime factorization of 6400 in exponential form is:

6400 = 2⁸ × 5²

Step-2: Prime Factorization of 6409

Prime factors of 6409 are 13, 17, 29. Prime factorization of 6409 in exponential form is:

6409 = 13¹ × 17¹ × 29¹

Step-3: Factors of 6400

List of positive integer factors of 6400 that divides 6400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 3200

Step-4: Factors of 6409

List of positive integer factors of 6409 that divides 6400 without a remainder.

1, 13, 17, 29, 221, 377, 493

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6400 and 6409. The biggest common factor number is the GCF number.
So the greatest common factor 6400 and 6409 is 1.

Also check out the Least Common Multiple of 6400 and 6409