What is the Greatest Common Factor of 8214 and 8229?

Greatest common factor (GCF) of 8214 and 8229 is 3.

GCF(8214,8229) = 3

We will now calculate the prime factors of 8214 and 8229, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8214 and 8229.

How to find the GCF of 8214 and 8229?

We will first find the prime factorization of 8214 and 8229. After we will calculate the factors of 8214 and 8229 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 8229

Prime factors of 8229 are 3, 13, 211. Prime factorization of 8229 in exponential form is:

8229 = 3¹ × 13¹ × 211¹

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 8229

List of positive integer factors of 8229 that divides 8214 without a remainder.

1, 3, 13, 39, 211, 633, 2743

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8214 and 8229. The biggest common factor number is the GCF number.
So the greatest common factor 8214 and 8229 is 3.

Also check out the Least Common Multiple of 8214 and 8229