What is the Greatest Common Factor of 678 and 694?

Greatest common factor (GCF) of 678 and 694 is 2.

GCF(678,694) = 2

We will now calculate the prime factors of 678 and 694, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 694.

How to find the GCF of 678 and 694?

We will first find the prime factorization of 678 and 694. After we will calculate the factors of 678 and 694 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 694

Prime factors of 694 are 2, 347. Prime factorization of 694 in exponential form is:

694 = 2¹ × 347¹

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 694

List of positive integer factors of 694 that divides 678 without a remainder.

1, 2, 347

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 694. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 694 is 2.

Also check out the Least Common Multiple of 678 and 694