What is the Greatest Common Factor of 677 and 688?

Greatest common factor (GCF) of 677 and 688 is 1.

GCF(677,688) = 1

We will now calculate the prime factors of 677 and 688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 677 and 688.

How to find the GCF of 677 and 688?

We will first find the prime factorization of 677 and 688. After we will calculate the factors of 677 and 688 and find the biggest common factor number .

Step-1: Prime Factorization of 677

Prime factors of 677 are 677. Prime factorization of 677 in exponential form is:

677 = 677¹

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 677

List of positive integer factors of 677 that divides 677 without a remainder.

Step-4: Factors of 688

List of positive integer factors of 688 that divides 677 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 677 and 688. The biggest common factor number is the GCF number.
So the greatest common factor 677 and 688 is 1.

Also check out the Least Common Multiple of 677 and 688