What is the Greatest Common Factor of 680 and 690?

Greatest common factor (GCF) of 680 and 690 is 10.

GCF(680,690) = 10

We will now calculate the prime factors of 680 and 690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 680 and 690.

How to find the GCF of 680 and 690?

We will first find the prime factorization of 680 and 690. After we will calculate the factors of 680 and 690 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 690

Prime factors of 690 are 2, 3, 5, 23. Prime factorization of 690 in exponential form is:

690 = 2¹ × 3¹ × 5¹ × 23¹

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 690

List of positive integer factors of 690 that divides 680 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 680 and 690. The biggest common factor number is the GCF number.
So the greatest common factor 680 and 690 is 10.

Also check out the Least Common Multiple of 680 and 690