What is the Greatest Common Factor of 8200 and 8205?

Greatest common factor (GCF) of 8200 and 8205 is 5.

GCF(8200,8205) = 5

We will now calculate the prime factors of 8200 and 8205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8200 and 8205.

How to find the GCF of 8200 and 8205?

We will first find the prime factorization of 8200 and 8205. After we will calculate the factors of 8200 and 8205 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 8205

Prime factors of 8205 are 3, 5, 547. Prime factorization of 8205 in exponential form is:

8205 = 3¹ × 5¹ × 547¹

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 8205

List of positive integer factors of 8205 that divides 8200 without a remainder.

1, 3, 5, 15, 547, 1641, 2735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8200 and 8205. The biggest common factor number is the GCF number.
So the greatest common factor 8200 and 8205 is 5.

Also check out the Least Common Multiple of 8200 and 8205