What is the Greatest Common Factor of 54180 and 54200?

Greatest common factor (GCF) of 54180 and 54200 is 20.

GCF(54180,54200) = 20

We will now calculate the prime factors of 54180 and 54200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54180 and 54200.

How to find the GCF of 54180 and 54200?

We will first find the prime factorization of 54180 and 54200. After we will calculate the factors of 54180 and 54200 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 54200

Prime factors of 54200 are 2, 5, 271. Prime factorization of 54200 in exponential form is:

54200 = 2³ × 5² × 271¹

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 54200

List of positive integer factors of 54200 that divides 54180 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 271, 542, 1084, 1355, 2168, 2710, 5420, 6775, 10840, 13550, 27100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54180 and 54200. The biggest common factor number is the GCF number.
So the greatest common factor 54180 and 54200 is 20.

Also check out the Least Common Multiple of 54180 and 54200