What is the Greatest Common Factor of 54590 and 54600?

Greatest common factor (GCF) of 54590 and 54600 is 10.

GCF(54590,54600) = 10

We will now calculate the prime factors of 54590 and 54600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54590 and 54600.

How to find the GCF of 54590 and 54600?

We will first find the prime factorization of 54590 and 54600. After we will calculate the factors of 54590 and 54600 and find the biggest common factor number .

Step-1: Prime Factorization of 54590

Prime factors of 54590 are 2, 5, 53, 103. Prime factorization of 54590 in exponential form is:

54590 = 2¹ × 5¹ × 53¹ × 103¹

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 54590

List of positive integer factors of 54590 that divides 54590 without a remainder.

1, 2, 5, 10, 53, 103, 106, 206, 265, 515, 530, 1030, 5459, 10918, 27295

Step-4: Factors of 54600

List of positive integer factors of 54600 that divides 54590 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 54590 and 54600. The biggest common factor number is the GCF number.
So the greatest common factor 54590 and 54600 is 10.

Also check out the Least Common Multiple of 54590 and 54600