What is the Greatest Common Factor of 189 and 204?

Greatest common factor (GCF) of 189 and 204 is 3.

GCF(189,204) = 3

We will now calculate the prime factors of 189 and 204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 189 and 204.

How to find the GCF of 189 and 204?

We will first find the prime factorization of 189 and 204. After we will calculate the factors of 189 and 204 and find the biggest common factor number .

Step-1: Prime Factorization of 189

Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:

189 = 3³ × 7¹

Step-2: 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-3: Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63

Step-4: Factors of 204

List of positive integer factors of 204 that divides 189 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 189 and 204. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 204 is 3.

Also check out the Least Common Multiple of 189 and 204