What is the Greatest Common Factor of 204 and 214?

Greatest common factor (GCF) of 204 and 214 is 2.

GCF(204,214) = 2

We will now calculate the prime factors of 204 and 214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 204 and 214.

How to find the GCF of 204 and 214?

We will first find the prime factorization of 204 and 214. After we will calculate the factors of 204 and 214 and find the biggest common factor number .

Step-1: Prime Factorization of 204

Prime factors of 204 are 2, 3, 17. Prime factorization of 204 in exponential form is:

204 = 2² × 3¹ × 17¹

Step-2: Prime Factorization of 214

Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:

214 = 2¹ × 107¹

Step-3: Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102

Step-4: Factors of 214

List of positive integer factors of 214 that divides 204 without a remainder.

1, 2, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 204 and 214. The biggest common factor number is the GCF number.
So the greatest common factor 204 and 214 is 2.

Also check out the Least Common Multiple of 204 and 214