What is the Greatest Common Factor of 800 and 812?

Greatest common factor (GCF) of 800 and 812 is 4.

GCF(800,812) = 4

We will now calculate the prime factors of 800 and 812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 800 and 812.

How to find the GCF of 800 and 812?

We will first find the prime factorization of 800 and 812. After we will calculate the factors of 800 and 812 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 812

Prime factors of 812 are 2, 7, 29. Prime factorization of 812 in exponential form is:

812 = 2² × 7¹ × 29¹

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 812

List of positive integer factors of 812 that divides 800 without a remainder.

1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 800 and 812. The biggest common factor number is the GCF number.
So the greatest common factor 800 and 812 is 4.

Also check out the Least Common Multiple of 800 and 812