What is the Greatest Common Factor of 666 and 684?

Greatest common factor (GCF) of 666 and 684 is 18.

GCF(666,684) = 18

We will now calculate the prime factors of 666 and 684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 666 and 684.

How to find the GCF of 666 and 684?

We will first find the prime factorization of 666 and 684. After we will calculate the factors of 666 and 684 and find the biggest common factor number .

Step-1: Prime Factorization of 666

Prime factors of 666 are 2, 3, 37. Prime factorization of 666 in exponential form is:

666 = 2¹ × 3² × 37¹

Step-2: Prime Factorization of 684

Prime factors of 684 are 2, 3, 19. Prime factorization of 684 in exponential form is:

684 = 2² × 3² × 19¹

Step-3: Factors of 666

List of positive integer factors of 666 that divides 666 without a remainder.

1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333

Step-4: Factors of 684

List of positive integer factors of 684 that divides 666 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 666 and 684. The biggest common factor number is the GCF number.
So the greatest common factor 666 and 684 is 18.

Also check out the Least Common Multiple of 666 and 684