What is the Greatest Common Factor of 204 and 221?

Greatest common factor (GCF) of 204 and 221 is 17.

GCF(204,221) = 17

We will now calculate the prime factors of 204 and 221, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 204 and 221.

How to find the GCF of 204 and 221?

We will first find the prime factorization of 204 and 221. After we will calculate the factors of 204 and 221 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 221

Prime factors of 221 are 13, 17. Prime factorization of 221 in exponential form is:

221 = 13¹ × 17¹

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 221

List of positive integer factors of 221 that divides 204 without a remainder.

1, 13, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 204 and 221. The biggest common factor number is the GCF number.
So the greatest common factor 204 and 221 is 17.

Also check out the Least Common Multiple of 204 and 221