What is the Greatest Common Factor of 680 and 684?

Greatest common factor (GCF) of 680 and 684 is 4.

GCF(680,684) = 4

We will now calculate the prime factors of 680 and 684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 680 and 684.

How to find the GCF of 680 and 684?

We will first find the prime factorization of 680 and 684. After we will calculate the factors of 680 and 684 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 684

Prime factors of 684 are 2, 3, 19. Prime factorization of 684 in exponential form is:

684 = 2² × 3² × 19¹

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 684

List of positive integer factors of 684 that divides 680 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 680 and 684. The biggest common factor number is the GCF number.
So the greatest common factor 680 and 684 is 4.

Also check out the Least Common Multiple of 680 and 684