What is the Greatest Common Factor of 8200 and 8210?

Greatest common factor (GCF) of 8200 and 8210 is 10.

GCF(8200,8210) = 10

We will now calculate the prime factors of 8200 and 8210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8200 and 8210.

How to find the GCF of 8200 and 8210?

We will first find the prime factorization of 8200 and 8210. After we will calculate the factors of 8200 and 8210 and find the biggest common factor number .

Step-1: Prime Factorization of 8200

Prime factors of 8200 are 2, 5, 41. Prime factorization of 8200 in exponential form is:

8200 = 2³ × 5² × 41¹

Step-2: Prime Factorization of 8210

Prime factors of 8210 are 2, 5, 821. Prime factorization of 8210 in exponential form is:

8210 = 2¹ × 5¹ × 821¹

Step-3: Factors of 8200

List of positive integer factors of 8200 that divides 8200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 41, 50, 82, 100, 164, 200, 205, 328, 410, 820, 1025, 1640, 2050, 4100

Step-4: Factors of 8210

List of positive integer factors of 8210 that divides 8200 without a remainder.

1, 2, 5, 10, 821, 1642, 4105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8200 and 8210. The biggest common factor number is the GCF number.
So the greatest common factor 8200 and 8210 is 10.

Also check out the Least Common Multiple of 8200 and 8210