What is the Greatest Common Factor of 13678 and 13686?

Greatest common factor (GCF) of 13678 and 13686 is 2.

GCF(13678,13686) = 2

We will now calculate the prime factors of 13678 and 13686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13678 and 13686.

How to find the GCF of 13678 and 13686?

We will first find the prime factorization of 13678 and 13686. After we will calculate the factors of 13678 and 13686 and find the biggest common factor number .

Step-1: Prime Factorization of 13678

Prime factors of 13678 are 2, 7, 977. Prime factorization of 13678 in exponential form is:

13678 = 2¹ × 7¹ × 977¹

Step-2: Prime Factorization of 13686

Prime factors of 13686 are 2, 3, 2281. Prime factorization of 13686 in exponential form is:

13686 = 2¹ × 3¹ × 2281¹

Step-3: Factors of 13678

List of positive integer factors of 13678 that divides 13678 without a remainder.

1, 2, 7, 14, 977, 1954, 6839

Step-4: Factors of 13686

List of positive integer factors of 13686 that divides 13678 without a remainder.

1, 2, 3, 6, 2281, 4562, 6843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13678 and 13686. The biggest common factor number is the GCF number.
So the greatest common factor 13678 and 13686 is 2.

Also check out the Least Common Multiple of 13678 and 13686