What is the Greatest Common Factor of 678 and 687?

Greatest common factor (GCF) of 678 and 687 is 3.

GCF(678,687) = 3

We will now calculate the prime factors of 678 and 687, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 687.

How to find the GCF of 678 and 687?

We will first find the prime factorization of 678 and 687. After we will calculate the factors of 678 and 687 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 687

Prime factors of 687 are 3, 229. Prime factorization of 687 in exponential form is:

687 = 3¹ × 229¹

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 687

List of positive integer factors of 687 that divides 678 without a remainder.

1, 3, 229

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 687. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 687 is 3.

Also check out the Least Common Multiple of 678 and 687