What is the Greatest Common Factor of 185 and 189?

Greatest common factor (GCF) of 185 and 189 is 1.

GCF(185,189) = 1

We will now calculate the prime factors of 185 and 189, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 185 and 189.

How to find the GCF of 185 and 189?

We will first find the prime factorization of 185 and 189. After we will calculate the factors of 185 and 189 and find the biggest common factor number .

Step-1: Prime Factorization of 185

Prime factors of 185 are 5, 37. Prime factorization of 185 in exponential form is:

185 = 5¹ × 37¹

Step-2: Prime Factorization of 189

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

189 = 3³ × 7¹

Step-3: Factors of 185

List of positive integer factors of 185 that divides 185 without a remainder.

1, 5, 37

Step-4: Factors of 189

List of positive integer factors of 189 that divides 185 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 185 and 189. The biggest common factor number is the GCF number.
So the greatest common factor 185 and 189 is 1.

Also check out the Least Common Multiple of 185 and 189