What is the Greatest Common Factor of 13665 and 13674?

Greatest common factor (GCF) of 13665 and 13674 is 3.

GCF(13665,13674) = 3

We will now calculate the prime factors of 13665 and 13674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13665 and 13674.

How to find the GCF of 13665 and 13674?

We will first find the prime factorization of 13665 and 13674. After we will calculate the factors of 13665 and 13674 and find the biggest common factor number .

Step-1: Prime Factorization of 13665

Prime factors of 13665 are 3, 5, 911. Prime factorization of 13665 in exponential form is:

13665 = 3¹ × 5¹ × 911¹

Step-2: 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-3: Factors of 13665

List of positive integer factors of 13665 that divides 13665 without a remainder.

1, 3, 5, 15, 911, 2733, 4555

Step-4: Factors of 13674

List of positive integer factors of 13674 that divides 13665 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13665 and 13674. The biggest common factor number is the GCF number.
So the greatest common factor 13665 and 13674 is 3.

Also check out the Least Common Multiple of 13665 and 13674