What is the Greatest Common Factor of 13186 and 13205?

Greatest common factor (GCF) of 13186 and 13205 is 19.

GCF(13186,13205) = 19

We will now calculate the prime factors of 13186 and 13205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13186 and 13205.

How to find the GCF of 13186 and 13205?

We will first find the prime factorization of 13186 and 13205. After we will calculate the factors of 13186 and 13205 and find the biggest common factor number .

Step-1: Prime Factorization of 13186

Prime factors of 13186 are 2, 19, 347. Prime factorization of 13186 in exponential form is:

13186 = 2¹ × 19¹ × 347¹

Step-2: Prime Factorization of 13205

Prime factors of 13205 are 5, 19, 139. Prime factorization of 13205 in exponential form is:

13205 = 5¹ × 19¹ × 139¹

Step-3: Factors of 13186

List of positive integer factors of 13186 that divides 13186 without a remainder.

1, 2, 19, 38, 347, 694, 6593

Step-4: Factors of 13205

List of positive integer factors of 13205 that divides 13186 without a remainder.

1, 5, 19, 95, 139, 695, 2641

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13186 and 13205. The biggest common factor number is the GCF number.
So the greatest common factor 13186 and 13205 is 19.

Also check out the Least Common Multiple of 13186 and 13205