What is the Greatest Common Factor of 678 and 684?

Greatest common factor (GCF) of 678 and 684 is 6.

GCF(678,684) = 6

We will now calculate the prime factors of 678 and 684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 684.

How to find the GCF of 678 and 684?

We will first find the prime factorization of 678 and 684. After we will calculate the factors of 678 and 684 and find the biggest common factor number .

Step-1: Prime Factorization of 678

Prime factors of 678 are 2, 3, 113. Prime factorization of 678 in exponential form is:

678 = 2¹ × 3¹ × 113¹

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 678

List of positive integer factors of 678 that divides 678 without a remainder.

1, 2, 3, 6, 113, 226, 339

Step-4: Factors of 684

List of positive integer factors of 684 that divides 678 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 678 and 684. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 684 is 6.

Also check out the Least Common Multiple of 678 and 684