What is the Greatest Common Factor of 54180 and 54190?

Greatest common factor (GCF) of 54180 and 54190 is 10.

GCF(54180,54190) = 10

We will now calculate the prime factors of 54180 and 54190, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54180 and 54190.

How to find the GCF of 54180 and 54190?

We will first find the prime factorization of 54180 and 54190. After we will calculate the factors of 54180 and 54190 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 54190

Prime factors of 54190 are 2, 5, 5419. Prime factorization of 54190 in exponential form is:

54190 = 2¹ × 5¹ × 5419¹

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 54190

List of positive integer factors of 54190 that divides 54180 without a remainder.

1, 2, 5, 10, 5419, 10838, 27095

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54180 and 54190. The biggest common factor number is the GCF number.
So the greatest common factor 54180 and 54190 is 10.

Also check out the Least Common Multiple of 54180 and 54190