What is the Greatest Common Factor of 6400 and 6405?

Greatest common factor (GCF) of 6400 and 6405 is 5.

GCF(6400,6405) = 5

We will now calculate the prime factors of 6400 and 6405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6400 and 6405.

How to find the GCF of 6400 and 6405?

We will first find the prime factorization of 6400 and 6405. After we will calculate the factors of 6400 and 6405 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 6405

Prime factors of 6405 are 3, 5, 7, 61. Prime factorization of 6405 in exponential form is:

6405 = 3¹ × 5¹ × 7¹ × 61¹

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 6405

List of positive integer factors of 6405 that divides 6400 without a remainder.

1, 3, 5, 7, 15, 21, 35, 61, 105, 183, 305, 427, 915, 1281, 2135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6400 and 6405. The biggest common factor number is the GCF number.
So the greatest common factor 6400 and 6405 is 5.

Also check out the Least Common Multiple of 6400 and 6405