What is the Greatest Common Factor of 680 and 697?

Greatest common factor (GCF) of 680 and 697 is 17.

GCF(680,697) = 17

We will now calculate the prime factors of 680 and 697, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 680 and 697.

How to find the GCF of 680 and 697?

We will first find the prime factorization of 680 and 697. After we will calculate the factors of 680 and 697 and find the biggest common factor number .

Step-1: Prime Factorization of 680

Prime factors of 680 are 2, 5, 17. Prime factorization of 680 in exponential form is:

680 = 2³ × 5¹ × 17¹

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 680

List of positive integer factors of 680 that divides 680 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340

Step-4: Factors of 697

List of positive integer factors of 697 that divides 680 without a remainder.

1, 17, 41

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 680 and 697. The biggest common factor number is the GCF number.
So the greatest common factor 680 and 697 is 17.

Also check out the Least Common Multiple of 680 and 697