What is the Greatest Common Factor of 800 and 819?

Greatest common factor (GCF) of 800 and 819 is 1.

GCF(800,819) = 1

We will now calculate the prime factors of 800 and 819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 800 and 819.

How to find the GCF of 800 and 819?

We will first find the prime factorization of 800 and 819. After we will calculate the factors of 800 and 819 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 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 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 819

List of positive integer factors of 819 that divides 800 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 800 and 819. The biggest common factor number is the GCF number.
So the greatest common factor 800 and 819 is 1.

Also check out the Least Common Multiple of 800 and 819