What is the Greatest Common Factor of 810 and 828?

Greatest common factor (GCF) of 810 and 828 is 18.

GCF(810,828) = 18

We will now calculate the prime factors of 810 and 828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 810 and 828.

How to find the GCF of 810 and 828?

We will first find the prime factorization of 810 and 828. After we will calculate the factors of 810 and 828 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 828

Prime factors of 828 are 2, 3, 23. Prime factorization of 828 in exponential form is:

828 = 2² × 3² × 23¹

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 828

List of positive integer factors of 828 that divides 810 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 810 and 828. The biggest common factor number is the GCF number.
So the greatest common factor 810 and 828 is 18.

Also check out the Least Common Multiple of 810 and 828