What is the Greatest Common Factor of 13314 and 13321?

Greatest common factor (GCF) of 13314 and 13321 is 7.

GCF(13314,13321) = 7

We will now calculate the prime factors of 13314 and 13321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13314 and 13321.

How to find the GCF of 13314 and 13321?

We will first find the prime factorization of 13314 and 13321. After we will calculate the factors of 13314 and 13321 and find the biggest common factor number .

Step-1: Prime Factorization of 13314

Prime factors of 13314 are 2, 3, 7, 317. Prime factorization of 13314 in exponential form is:

13314 = 2¹ × 3¹ × 7¹ × 317¹

Step-2: Prime Factorization of 13321

Prime factors of 13321 are 7, 11, 173. Prime factorization of 13321 in exponential form is:

13321 = 7¹ × 11¹ × 173¹

Step-3: Factors of 13314

List of positive integer factors of 13314 that divides 13314 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 317, 634, 951, 1902, 2219, 4438, 6657

Step-4: Factors of 13321

List of positive integer factors of 13321 that divides 13314 without a remainder.

1, 7, 11, 77, 173, 1211, 1903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13314 and 13321. The biggest common factor number is the GCF number.
So the greatest common factor 13314 and 13321 is 7.

Also check out the Least Common Multiple of 13314 and 13321