What is the Greatest Common Factor of 6800 and 6814?

Greatest common factor (GCF) of 6800 and 6814 is 2.

GCF(6800,6814) = 2

We will now calculate the prime factors of 6800 and 6814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6800 and 6814.

How to find the GCF of 6800 and 6814?

We will first find the prime factorization of 6800 and 6814. After we will calculate the factors of 6800 and 6814 and find the biggest common factor number .

Step-1: Prime Factorization of 6800

Prime factors of 6800 are 2, 5, 17. Prime factorization of 6800 in exponential form is:

6800 = 2⁴ × 5² × 17¹

Step-2: Prime Factorization of 6814

Prime factors of 6814 are 2, 3407. Prime factorization of 6814 in exponential form is:

6814 = 2¹ × 3407¹

Step-3: Factors of 6800

List of positive integer factors of 6800 that divides 6800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 136, 170, 200, 272, 340, 400, 425, 680, 850, 1360, 1700, 3400

Step-4: Factors of 6814

List of positive integer factors of 6814 that divides 6800 without a remainder.

1, 2, 3407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6800 and 6814. The biggest common factor number is the GCF number.
So the greatest common factor 6800 and 6814 is 2.

Also check out the Least Common Multiple of 6800 and 6814