What is the Greatest Common Factor of 54165 and 54180?

Greatest common factor (GCF) of 54165 and 54180 is 15.

GCF(54165,54180) = 15

We will now calculate the prime factors of 54165 and 54180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54165 and 54180.

How to find the GCF of 54165 and 54180?

We will first find the prime factorization of 54165 and 54180. After we will calculate the factors of 54165 and 54180 and find the biggest common factor number .

Step-1: Prime Factorization of 54165

Prime factors of 54165 are 3, 5, 23, 157. Prime factorization of 54165 in exponential form is:

54165 = 3¹ × 5¹ × 23¹ × 157¹

Step-2: 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-3: Factors of 54165

List of positive integer factors of 54165 that divides 54165 without a remainder.

1, 3, 5, 15, 23, 69, 115, 157, 345, 471, 785, 2355, 3611, 10833, 18055

Step-4: Factors of 54180

List of positive integer factors of 54180 that divides 54165 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54165 and 54180. The biggest common factor number is the GCF number.
So the greatest common factor 54165 and 54180 is 15.

Also check out the Least Common Multiple of 54165 and 54180