What is the Greatest Common Factor of 678 and 689?

Greatest common factor (GCF) of 678 and 689 is 1.

GCF(678,689) = 1

We will now calculate the prime factors of 678 and 689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 678 and 689.

How to find the GCF of 678 and 689?

We will first find the prime factorization of 678 and 689. After we will calculate the factors of 678 and 689 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 689

Prime factors of 689 are 13, 53. Prime factorization of 689 in exponential form is:

689 = 13¹ × 53¹

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 689

List of positive integer factors of 689 that divides 678 without a remainder.

1, 13, 53

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 678 and 689. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 689 is 1.

Also check out the Least Common Multiple of 678 and 689