What is the Greatest Common Factor of 13202 and 13209?

Greatest common factor (GCF) of 13202 and 13209 is 7.

GCF(13202,13209) = 7

We will now calculate the prime factors of 13202 and 13209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13202 and 13209.

How to find the GCF of 13202 and 13209?

We will first find the prime factorization of 13202 and 13209. After we will calculate the factors of 13202 and 13209 and find the biggest common factor number .

Step-1: Prime Factorization of 13202

Prime factors of 13202 are 2, 7, 23, 41. Prime factorization of 13202 in exponential form is:

13202 = 2¹ × 7¹ × 23¹ × 41¹

Step-2: 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-3: Factors of 13202

List of positive integer factors of 13202 that divides 13202 without a remainder.

1, 2, 7, 14, 23, 41, 46, 82, 161, 287, 322, 574, 943, 1886, 6601

Step-4: Factors of 13209

List of positive integer factors of 13209 that divides 13202 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13202 and 13209. The biggest common factor number is the GCF number.
So the greatest common factor 13202 and 13209 is 7.

Also check out the Least Common Multiple of 13202 and 13209