What is the Greatest Common Factor of 678 and 692?

Greatest common factor (GCF) of 678 and 692 is 2.

GCF(678,692) = 2

We will now calculate the prime factors of 678 and 692, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 692.

How to find the GCF of 678 and 692?

We will first find the prime factorization of 678 and 692. After we will calculate the factors of 678 and 692 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 692

Prime factors of 692 are 2, 173. Prime factorization of 692 in exponential form is:

692 = 2² × 173¹

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 692

List of positive integer factors of 692 that divides 678 without a remainder.

1, 2, 4, 173, 346

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 692. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 692 is 2.

Also check out the Least Common Multiple of 678 and 692