What is the Greatest Common Factor of 13209 and 13216?

Greatest common factor (GCF) of 13209 and 13216 is 7.

GCF(13209,13216) = 7

We will now calculate the prime factors of 13209 and 13216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13209 and 13216.

How to find the GCF of 13209 and 13216?

We will first find the prime factorization of 13209 and 13216. After we will calculate the factors of 13209 and 13216 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 13216

Prime factors of 13216 are 2, 7, 59. Prime factorization of 13216 in exponential form is:

13216 = 2⁵ × 7¹ × 59¹

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 13216

List of positive integer factors of 13216 that divides 13209 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 59, 112, 118, 224, 236, 413, 472, 826, 944, 1652, 1888, 3304, 6608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13209 and 13216. The biggest common factor number is the GCF number.
So the greatest common factor 13209 and 13216 is 7.

Also check out the Least Common Multiple of 13209 and 13216