What is the Greatest Common Factor of 3667 and 3686?

Greatest common factor (GCF) of 3667 and 3686 is 19.

GCF(3667,3686) = 19

We will now calculate the prime factors of 3667 and 3686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3667 and 3686.

How to find the GCF of 3667 and 3686?

We will first find the prime factorization of 3667 and 3686. After we will calculate the factors of 3667 and 3686 and find the biggest common factor number .

Step-1: Prime Factorization of 3667

Prime factors of 3667 are 19, 193. Prime factorization of 3667 in exponential form is:

3667 = 19¹ × 193¹

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 3667

List of positive integer factors of 3667 that divides 3667 without a remainder.

1, 19, 193

Step-4: Factors of 3686

List of positive integer factors of 3686 that divides 3667 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3667 and 3686. The biggest common factor number is the GCF number.
So the greatest common factor 3667 and 3686 is 19.

Also check out the Least Common Multiple of 3667 and 3686