What is the Greatest Common Factor of 13509 and 13514?

Greatest common factor (GCF) of 13509 and 13514 is 1.

GCF(13509,13514) = 1

We will now calculate the prime factors of 13509 and 13514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13509 and 13514.

How to find the GCF of 13509 and 13514?

We will first find the prime factorization of 13509 and 13514. After we will calculate the factors of 13509 and 13514 and find the biggest common factor number .

Step-1: Prime Factorization of 13509

Prime factors of 13509 are 3, 19, 79. Prime factorization of 13509 in exponential form is:

13509 = 3² × 19¹ × 79¹

Step-2: Prime Factorization of 13514

Prime factors of 13514 are 2, 29, 233. Prime factorization of 13514 in exponential form is:

13514 = 2¹ × 29¹ × 233¹

Step-3: Factors of 13509

List of positive integer factors of 13509 that divides 13509 without a remainder.

1, 3, 9, 19, 57, 79, 171, 237, 711, 1501, 4503

Step-4: Factors of 13514

List of positive integer factors of 13514 that divides 13509 without a remainder.

1, 2, 29, 58, 233, 466, 6757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13509 and 13514. The biggest common factor number is the GCF number.
So the greatest common factor 13509 and 13514 is 1.

Also check out the Least Common Multiple of 13509 and 13514