What is the Greatest Common Factor of 688 and 697?

Greatest common factor (GCF) of 688 and 697 is 1.

GCF(688,697) = 1

We will now calculate the prime factors of 688 and 697, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 688 and 697.

How to find the GCF of 688 and 697?

We will first find the prime factorization of 688 and 697. After we will calculate the factors of 688 and 697 and find the biggest common factor number .

Step-1: Prime Factorization of 688

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

688 = 2⁴ × 43¹

Step-2: Prime Factorization of 697

Prime factors of 697 are 17, 41. Prime factorization of 697 in exponential form is:

697 = 17¹ × 41¹

Step-3: Factors of 688

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

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

Step-4: Factors of 697

List of positive integer factors of 697 that divides 688 without a remainder.

1, 17, 41

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 688 and 697. The biggest common factor number is the GCF number.
So the greatest common factor 688 and 697 is 1.

Also check out the Least Common Multiple of 688 and 697