What is the Greatest Common Factor of 8214 and 8227?

Greatest common factor (GCF) of 8214 and 8227 is 1.

GCF(8214,8227) = 1

We will now calculate the prime factors of 8214 and 8227, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8214 and 8227.

How to find the GCF of 8214 and 8227?

We will first find the prime factorization of 8214 and 8227. After we will calculate the factors of 8214 and 8227 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 8227

Prime factors of 8227 are 19, 433. Prime factorization of 8227 in exponential form is:

8227 = 19¹ × 433¹

Step-3: Factors of 8214

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

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

Step-4: Factors of 8227

List of positive integer factors of 8227 that divides 8214 without a remainder.

1, 19, 433

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8214 and 8227. The biggest common factor number is the GCF number.
So the greatest common factor 8214 and 8227 is 1.

Also check out the Least Common Multiple of 8214 and 8227