What is the Greatest Common Factor of 36180 and 36192?

Greatest common factor (GCF) of 36180 and 36192 is 12.

GCF(36180,36192) = 12

We will now calculate the prime factors of 36180 and 36192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36180 and 36192.

How to find the GCF of 36180 and 36192?

We will first find the prime factorization of 36180 and 36192. After we will calculate the factors of 36180 and 36192 and find the biggest common factor number .

Step-1: Prime Factorization of 36180

Prime factors of 36180 are 2, 3, 5, 67. Prime factorization of 36180 in exponential form is:

36180 = 2² × 3³ × 5¹ × 67¹

Step-2: 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-3: Factors of 36180

List of positive integer factors of 36180 that divides 36180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 67, 90, 108, 134, 135, 180, 201, 268, 270, 335, 402, 540, 603, 670, 804, 1005, 1206, 1340, 1809, 2010, 2412, 3015, 3618, 4020, 6030, 7236, 9045, 12060, 18090

Step-4: Factors of 36192

List of positive integer factors of 36192 that divides 36180 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36180 and 36192. The biggest common factor number is the GCF number.
So the greatest common factor 36180 and 36192 is 12.

Also check out the Least Common Multiple of 36180 and 36192