What is the Greatest Common Factor of 3686 and 3705?

Greatest common factor (GCF) of 3686 and 3705 is 19.

GCF(3686,3705) = 19

We will now calculate the prime factors of 3686 and 3705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3686 and 3705.

How to find the GCF of 3686 and 3705?

We will first find the prime factorization of 3686 and 3705. After we will calculate the factors of 3686 and 3705 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 3705

Prime factors of 3705 are 3, 5, 13, 19. Prime factorization of 3705 in exponential form is:

3705 = 3¹ × 5¹ × 13¹ × 19¹

Step-3: Factors of 3686

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

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

Step-4: Factors of 3705

List of positive integer factors of 3705 that divides 3686 without a remainder.

1, 3, 5, 13, 15, 19, 39, 57, 65, 95, 195, 247, 285, 741, 1235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3686 and 3705. The biggest common factor number is the GCF number.
So the greatest common factor 3686 and 3705 is 19.

Also check out the Least Common Multiple of 3686 and 3705