What is the Greatest Common Factor of 54600 and 54612?

Greatest common factor (GCF) of 54600 and 54612 is 12.

GCF(54600,54612) = 12

We will now calculate the prime factors of 54600 and 54612, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54600 and 54612.

How to find the GCF of 54600 and 54612?

We will first find the prime factorization of 54600 and 54612. After we will calculate the factors of 54600 and 54612 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54612

Prime factors of 54612 are 2, 3, 37, 41. Prime factorization of 54612 in exponential form is:

54612 = 2² × 3² × 37¹ × 41¹

Step-3: Factors of 54600

List of positive integer factors of 54600 that divides 54600 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

Step-4: Factors of 54612

List of positive integer factors of 54612 that divides 54600 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 37, 41, 74, 82, 111, 123, 148, 164, 222, 246, 333, 369, 444, 492, 666, 738, 1332, 1476, 1517, 3034, 4551, 6068, 9102, 13653, 18204, 27306

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54600 and 54612. The biggest common factor number is the GCF number.
So the greatest common factor 54600 and 54612 is 12.

Also check out the Least Common Multiple of 54600 and 54612