What is the Greatest Common Factor of 3680 and 3686?

Greatest common factor (GCF) of 3680 and 3686 is 2.

GCF(3680,3686) = 2

We will now calculate the prime factors of 3680 and 3686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3680 and 3686.

How to find the GCF of 3680 and 3686?

We will first find the prime factorization of 3680 and 3686. After we will calculate the factors of 3680 and 3686 and find the biggest common factor number .

Step-1: Prime Factorization of 3680

Prime factors of 3680 are 2, 5, 23. Prime factorization of 3680 in exponential form is:

3680 = 2⁵ × 5¹ × 23¹

Step-2: Prime Factorization of 3686

Prime factors of 3686 are 2, 19, 97. Prime factorization of 3686 in exponential form is:

3686 = 2¹ × 19¹ × 97¹

Step-3: Factors of 3680

List of positive integer factors of 3680 that divides 3680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840

Step-4: Factors of 3686

List of positive integer factors of 3686 that divides 3680 without a remainder.

1, 2, 19, 38, 97, 194, 1843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3680 and 3686. The biggest common factor number is the GCF number.
So the greatest common factor 3680 and 3686 is 2.

Also check out the Least Common Multiple of 3680 and 3686