What is the Greatest Common Factor of 13674 and 13688?

Greatest common factor (GCF) of 13674 and 13688 is 2.

GCF(13674,13688) = 2

We will now calculate the prime factors of 13674 and 13688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13674 and 13688.

How to find the GCF of 13674 and 13688?

We will first find the prime factorization of 13674 and 13688. After we will calculate the factors of 13674 and 13688 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 13688

Prime factors of 13688 are 2, 29, 59. Prime factorization of 13688 in exponential form is:

13688 = 2³ × 29¹ × 59¹

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 13688

List of positive integer factors of 13688 that divides 13674 without a remainder.

1, 2, 4, 8, 29, 58, 59, 116, 118, 232, 236, 472, 1711, 3422, 6844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13674 and 13688. The biggest common factor number is the GCF number.
So the greatest common factor 13674 and 13688 is 2.

Also check out the Least Common Multiple of 13674 and 13688