What is the Greatest Common Factor of 810 and 819?

Greatest common factor (GCF) of 810 and 819 is 9.

GCF(810,819) = 9

We will now calculate the prime factors of 810 and 819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 810 and 819.

How to find the GCF of 810 and 819?

We will first find the prime factorization of 810 and 819. After we will calculate the factors of 810 and 819 and find the biggest common factor number .

Step-1: Prime Factorization of 810

Prime factors of 810 are 2, 3, 5. Prime factorization of 810 in exponential form is:

810 = 2¹ × 3⁴ × 5¹

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 810

List of positive integer factors of 810 that divides 810 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405

Step-4: Factors of 819

List of positive integer factors of 819 that divides 810 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 810 and 819. The biggest common factor number is the GCF number.
So the greatest common factor 810 and 819 is 9.

Also check out the Least Common Multiple of 810 and 819