What is the Greatest Common Factor of 13674 and 13678?

Greatest common factor (GCF) of 13674 and 13678 is 2.

GCF(13674,13678) = 2

We will now calculate the prime factors of 13674 and 13678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13674 and 13678.

How to find the GCF of 13674 and 13678?

We will first find the prime factorization of 13674 and 13678. After we will calculate the factors of 13674 and 13678 and find the biggest common factor number .

Step-1: Prime Factorization of 13674

Prime factors of 13674 are 2, 3, 43, 53. Prime factorization of 13674 in exponential form is:

13674 = 2¹ × 3¹ × 43¹ × 53¹

Step-2: 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-3: Factors of 13674

List of positive integer factors of 13674 that divides 13674 without a remainder.

1, 2, 3, 6, 43, 53, 86, 106, 129, 159, 258, 318, 2279, 4558, 6837

Step-4: Factors of 13678

List of positive integer factors of 13678 that divides 13674 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13674 and 13678. The biggest common factor number is the GCF number.
So the greatest common factor 13674 and 13678 is 2.

Also check out the Least Common Multiple of 13674 and 13678