What is the Greatest Common Factor of 809 and 814?

Greatest common factor (GCF) of 809 and 814 is 1.

GCF(809,814) = 1

We will now calculate the prime factors of 809 and 814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 809 and 814.

How to find the GCF of 809 and 814?

We will first find the prime factorization of 809 and 814. After we will calculate the factors of 809 and 814 and find the biggest common factor number .

Step-1: Prime Factorization of 809

Prime factors of 809 are 809. Prime factorization of 809 in exponential form is:

809 = 809¹

Step-2: Prime Factorization of 814

Prime factors of 814 are 2, 11, 37. Prime factorization of 814 in exponential form is:

814 = 2¹ × 11¹ × 37¹

Step-3: Factors of 809

List of positive integer factors of 809 that divides 809 without a remainder.

Step-4: Factors of 814

List of positive integer factors of 814 that divides 809 without a remainder.

1, 2, 11, 22, 37, 74, 407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 809 and 814. The biggest common factor number is the GCF number.
So the greatest common factor 809 and 814 is 1.

Also check out the Least Common Multiple of 809 and 814