What is the Greatest Common Factor of 800 and 820?

Greatest common factor (GCF) of 800 and 820 is 20.

GCF(800,820) = 20

We will now calculate the prime factors of 800 and 820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 800 and 820.

How to find the GCF of 800 and 820?

We will first find the prime factorization of 800 and 820. After we will calculate the factors of 800 and 820 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 820

Prime factors of 820 are 2, 5, 41. Prime factorization of 820 in exponential form is:

820 = 2² × 5¹ × 41¹

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 820

List of positive integer factors of 820 that divides 800 without a remainder.

1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 800 and 820. The biggest common factor number is the GCF number.
So the greatest common factor 800 and 820 is 20.

Also check out the Least Common Multiple of 800 and 820