What is the Greatest Common Factor of 800 and 810?

Greatest common factor (GCF) of 800 and 810 is 10.

GCF(800,810) = 10

We will now calculate the prime factors of 800 and 810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 800 and 810.

How to find the GCF of 800 and 810?

We will first find the prime factorization of 800 and 810. After we will calculate the factors of 800 and 810 and find the biggest common factor number .

Step-1: Prime Factorization of 800

Prime factors of 800 are 2, 5. Prime factorization of 800 in exponential form is:

800 = 2⁵ × 5²

Step-2: 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-3: Factors of 800

List of positive integer factors of 800 that divides 800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400

Step-4: Factors of 810

List of positive integer factors of 810 that divides 800 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 800 and 810. The biggest common factor number is the GCF number.
So the greatest common factor 800 and 810 is 10.

Also check out the Least Common Multiple of 800 and 810