What is the Greatest Common Factor of 198 and 210?

Greatest common factor (GCF) of 198 and 210 is 6.

GCF(198,210) = 6

We will now calculate the prime factors of 198 and 210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 198 and 210.

How to find the GCF of 198 and 210?

We will first find the prime factorization of 198 and 210. After we will calculate the factors of 198 and 210 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 210

Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:

210 = 2¹ × 3¹ × 5¹ × 7¹

Step-3: Factors of 198

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

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

Step-4: Factors of 210

List of positive integer factors of 210 that divides 198 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 198 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 198 and 210 is 6.

Also check out the Least Common Multiple of 198 and 210