What is the Greatest Common Factor of 189 and 201?

Greatest common factor (GCF) of 189 and 201 is 3.

GCF(189,201) = 3

We will now calculate the prime factors of 189 and 201, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 189 and 201.

How to find the GCF of 189 and 201?

We will first find the prime factorization of 189 and 201. After we will calculate the factors of 189 and 201 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 201

Prime factors of 201 are 3, 67. Prime factorization of 201 in exponential form is:

201 = 3¹ × 67¹

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 201

List of positive integer factors of 201 that divides 189 without a remainder.

1, 3, 67

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 189 and 201. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 201 is 3.

Also check out the Least Common Multiple of 189 and 201