What is the Greatest Common Factor of 36192 and 36205?

Greatest common factor (GCF) of 36192 and 36205 is 13.

GCF(36192,36205) = 13

We will now calculate the prime factors of 36192 and 36205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36192 and 36205.

How to find the GCF of 36192 and 36205?

We will first find the prime factorization of 36192 and 36205. After we will calculate the factors of 36192 and 36205 and find the biggest common factor number .

Step-1: Prime Factorization of 36192

Prime factors of 36192 are 2, 3, 13, 29. Prime factorization of 36192 in exponential form is:

36192 = 2⁵ × 3¹ × 13¹ × 29¹

Step-2: Prime Factorization of 36205

Prime factors of 36205 are 5, 13, 557. Prime factorization of 36205 in exponential form is:

36205 = 5¹ × 13¹ × 557¹

Step-3: Factors of 36192

List of positive integer factors of 36192 that divides 36192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 29, 32, 39, 48, 52, 58, 78, 87, 96, 104, 116, 156, 174, 208, 232, 312, 348, 377, 416, 464, 624, 696, 754, 928, 1131, 1248, 1392, 1508, 2262, 2784, 3016, 4524, 6032, 9048, 12064, 18096

Step-4: Factors of 36205

List of positive integer factors of 36205 that divides 36192 without a remainder.

1, 5, 13, 65, 557, 2785, 7241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36192 and 36205. The biggest common factor number is the GCF number.
So the greatest common factor 36192 and 36205 is 13.

Also check out the Least Common Multiple of 36192 and 36205