What is the Greatest Common Factor of 54585 and 54600?

Greatest common factor (GCF) of 54585 and 54600 is 15.

GCF(54585,54600) = 15

We will now calculate the prime factors of 54585 and 54600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54585 and 54600.

How to find the GCF of 54585 and 54600?

We will first find the prime factorization of 54585 and 54600. After we will calculate the factors of 54585 and 54600 and find the biggest common factor number .

Step-1: Prime Factorization of 54585

Prime factors of 54585 are 3, 5, 1213. Prime factorization of 54585 in exponential form is:

54585 = 3² × 5¹ × 1213¹

Step-2: Prime Factorization of 54600

Prime factors of 54600 are 2, 3, 5, 7, 13. Prime factorization of 54600 in exponential form is:

54600 = 2³ × 3¹ × 5² × 7¹ × 13¹

Step-3: Factors of 54585

List of positive integer factors of 54585 that divides 54585 without a remainder.

1, 3, 5, 9, 15, 45, 1213, 3639, 6065, 10917, 18195

Step-4: Factors of 54600

List of positive integer factors of 54600 that divides 54585 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 20, 21, 24, 25, 26, 28, 30, 35, 39, 40, 42, 50, 52, 56, 60, 65, 70, 75, 78, 84, 91, 100, 104, 105, 120, 130, 140, 150, 156, 168, 175, 182, 195, 200, 210, 260, 273, 280, 300, 312, 325, 350, 364, 390, 420, 455, 520, 525, 546, 600, 650, 700, 728, 780, 840, 910, 975, 1050, 1092, 1300, 1365, 1400, 1560, 1820, 1950, 2100, 2184, 2275, 2600, 2730, 3640, 3900, 4200, 4550, 5460, 6825, 7800, 9100, 10920, 13650, 18200, 27300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54585 and 54600. The biggest common factor number is the GCF number.
So the greatest common factor 54585 and 54600 is 15.

Also check out the Least Common Multiple of 54585 and 54600