What is the Greatest Common Factor of 13509 and 13524?

Greatest common factor (GCF) of 13509 and 13524 is 3.

GCF(13509,13524) = 3

We will now calculate the prime factors of 13509 and 13524, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13509 and 13524.

How to find the GCF of 13509 and 13524?

We will first find the prime factorization of 13509 and 13524. After we will calculate the factors of 13509 and 13524 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 13524

Prime factors of 13524 are 2, 3, 7, 23. Prime factorization of 13524 in exponential form is:

13524 = 2² × 3¹ × 7² × 23¹

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 13524

List of positive integer factors of 13524 that divides 13509 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 49, 69, 84, 92, 98, 138, 147, 161, 196, 276, 294, 322, 483, 588, 644, 966, 1127, 1932, 2254, 3381, 4508, 6762

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13509 and 13524. The biggest common factor number is the GCF number.
So the greatest common factor 13509 and 13524 is 3.

Also check out the Least Common Multiple of 13509 and 13524