What is the Greatest Common Factor of 814 and 819?

Greatest common factor (GCF) of 814 and 819 is 1.

GCF(814,819) = 1

We will now calculate the prime factors of 814 and 819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 814 and 819.

How to find the GCF of 814 and 819?

We will first find the prime factorization of 814 and 819. After we will calculate the factors of 814 and 819 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 819

Prime factors of 819 are 3, 7, 13. Prime factorization of 819 in exponential form is:

819 = 3² × 7¹ × 13¹

Step-3: Factors of 814

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

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

Step-4: Factors of 819

List of positive integer factors of 819 that divides 814 without a remainder.

1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 814 and 819. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 819 is 1.

Also check out the Least Common Multiple of 814 and 819