What is the Greatest Common Factor of 13209 and 13221?

Greatest common factor (GCF) of 13209 and 13221 is 3.

GCF(13209,13221) = 3

We will now calculate the prime factors of 13209 and 13221, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13209 and 13221.

How to find the GCF of 13209 and 13221?

We will first find the prime factorization of 13209 and 13221. After we will calculate the factors of 13209 and 13221 and find the biggest common factor number .

Step-1: Prime Factorization of 13209

Prime factors of 13209 are 3, 7, 17, 37. Prime factorization of 13209 in exponential form is:

13209 = 3¹ × 7¹ × 17¹ × 37¹

Step-2: Prime Factorization of 13221

Prime factors of 13221 are 3, 13, 113. Prime factorization of 13221 in exponential form is:

13221 = 3² × 13¹ × 113¹

Step-3: Factors of 13209

List of positive integer factors of 13209 that divides 13209 without a remainder.

1, 3, 7, 17, 21, 37, 51, 111, 119, 259, 357, 629, 777, 1887, 4403

Step-4: Factors of 13221

List of positive integer factors of 13221 that divides 13209 without a remainder.

1, 3, 9, 13, 39, 113, 117, 339, 1017, 1469, 4407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13209 and 13221. The biggest common factor number is the GCF number.
So the greatest common factor 13209 and 13221 is 3.

Also check out the Least Common Multiple of 13209 and 13221