What is the Greatest Common Factor of 54180 and 54192?

Greatest common factor (GCF) of 54180 and 54192 is 12.

GCF(54180,54192) = 12

We will now calculate the prime factors of 54180 and 54192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54180 and 54192.

How to find the GCF of 54180 and 54192?

We will first find the prime factorization of 54180 and 54192. After we will calculate the factors of 54180 and 54192 and find the biggest common factor number .

Step-1: Prime Factorization of 54180

Prime factors of 54180 are 2, 3, 5, 7, 43. Prime factorization of 54180 in exponential form is:

54180 = 2² × 3² × 5¹ × 7¹ × 43¹

Step-2: Prime Factorization of 54192

Prime factors of 54192 are 2, 3, 1129. Prime factorization of 54192 in exponential form is:

54192 = 2⁴ × 3¹ × 1129¹

Step-3: Factors of 54180

List of positive integer factors of 54180 that divides 54180 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 43, 45, 60, 63, 70, 84, 86, 90, 105, 126, 129, 140, 172, 180, 210, 215, 252, 258, 301, 315, 387, 420, 430, 516, 602, 630, 645, 774, 860, 903, 1204, 1260, 1290, 1505, 1548, 1806, 1935, 2580, 2709, 3010, 3612, 3870, 4515, 5418, 6020, 7740, 9030, 10836, 13545, 18060, 27090

Step-4: Factors of 54192

List of positive integer factors of 54192 that divides 54180 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1129, 2258, 3387, 4516, 6774, 9032, 13548, 18064, 27096

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54180 and 54192. The biggest common factor number is the GCF number.
So the greatest common factor 54180 and 54192 is 12.

Also check out the Least Common Multiple of 54180 and 54192