What is the Greatest Common Factor of 13205 and 13224?

Greatest common factor (GCF) of 13205 and 13224 is 19.

GCF(13205,13224) = 19

We will now calculate the prime factors of 13205 and 13224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13205 and 13224.

How to find the GCF of 13205 and 13224?

We will first find the prime factorization of 13205 and 13224. After we will calculate the factors of 13205 and 13224 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13224

Prime factors of 13224 are 2, 3, 19, 29. Prime factorization of 13224 in exponential form is:

13224 = 2³ × 3¹ × 19¹ × 29¹

Step-3: Factors of 13205

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

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

Step-4: Factors of 13224

List of positive integer factors of 13224 that divides 13205 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 29, 38, 57, 58, 76, 87, 114, 116, 152, 174, 228, 232, 348, 456, 551, 696, 1102, 1653, 2204, 3306, 4408, 6612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13205 and 13224. The biggest common factor number is the GCF number.
So the greatest common factor 13205 and 13224 is 19.

Also check out the Least Common Multiple of 13205 and 13224