What is the Greatest Common Factor of 678 and 688?

Greatest common factor (GCF) of 678 and 688 is 2.

GCF(678,688) = 2

We will now calculate the prime factors of 678 and 688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 688.

How to find the GCF of 678 and 688?

We will first find the prime factorization of 678 and 688. After we will calculate the factors of 678 and 688 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 688

Prime factors of 688 are 2, 43. Prime factorization of 688 in exponential form is:

688 = 2⁴ × 43¹

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 688

List of positive integer factors of 688 that divides 678 without a remainder.

1, 2, 4, 8, 16, 43, 86, 172, 344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 688. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 688 is 2.

Also check out the Least Common Multiple of 678 and 688