What is the Greatest Common Factor of 680 and 694?

Greatest common factor (GCF) of 680 and 694 is 2.

GCF(680,694) = 2

We will now calculate the prime factors of 680 and 694, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 680 and 694.

How to find the GCF of 680 and 694?

We will first find the prime factorization of 680 and 694. After we will calculate the factors of 680 and 694 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 694

Prime factors of 694 are 2, 347. Prime factorization of 694 in exponential form is:

694 = 2¹ × 347¹

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 694

List of positive integer factors of 694 that divides 680 without a remainder.

1, 2, 347

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 680 and 694. The biggest common factor number is the GCF number.
So the greatest common factor 680 and 694 is 2.

Also check out the Least Common Multiple of 680 and 694