What is the Greatest Common Factor of 678 and 682?

Greatest common factor (GCF) of 678 and 682 is 2.

GCF(678,682) = 2

We will now calculate the prime factors of 678 and 682, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 682.

How to find the GCF of 678 and 682?

We will first find the prime factorization of 678 and 682. After we will calculate the factors of 678 and 682 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 682

Prime factors of 682 are 2, 11, 31. Prime factorization of 682 in exponential form is:

682 = 2¹ × 11¹ × 31¹

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 682

List of positive integer factors of 682 that divides 678 without a remainder.

1, 2, 11, 22, 31, 62, 341

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 682. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 682 is 2.

Also check out the Least Common Multiple of 678 and 682