What is the Greatest Common Factor of 186 and 198?

Greatest common factor (GCF) of 186 and 198 is 6.

GCF(186,198) = 6

We will now calculate the prime factors of 186 and 198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 186 and 198.

How to find the GCF of 186 and 198?

We will first find the prime factorization of 186 and 198. After we will calculate the factors of 186 and 198 and find the biggest common factor number .

Step-1: Prime Factorization of 186

Prime factors of 186 are 2, 3, 31. Prime factorization of 186 in exponential form is:

186 = 2¹ × 3¹ × 31¹

Step-2: Prime Factorization of 198

Prime factors of 198 are 2, 3, 11. Prime factorization of 198 in exponential form is:

198 = 2¹ × 3² × 11¹

Step-3: Factors of 186

List of positive integer factors of 186 that divides 186 without a remainder.

1, 2, 3, 6, 31, 62, 93

Step-4: Factors of 198

List of positive integer factors of 198 that divides 186 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 186 and 198. The biggest common factor number is the GCF number.
So the greatest common factor 186 and 198 is 6.

Also check out the Least Common Multiple of 186 and 198