What is the Greatest Common Factor of 8205 and 8214?

Greatest common factor (GCF) of 8205 and 8214 is 3.

GCF(8205,8214) = 3

We will now calculate the prime factors of 8205 and 8214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8205 and 8214.

How to find the GCF of 8205 and 8214?

We will first find the prime factorization of 8205 and 8214. After we will calculate the factors of 8205 and 8214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 8214

Prime factors of 8214 are 2, 3, 37. Prime factorization of 8214 in exponential form is:

8214 = 2¹ × 3¹ × 37²

Step-3: Factors of 8205

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

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

Step-4: Factors of 8214

List of positive integer factors of 8214 that divides 8205 without a remainder.

1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8205 and 8214. The biggest common factor number is the GCF number.
So the greatest common factor 8205 and 8214 is 3.

Also check out the Least Common Multiple of 8205 and 8214