What is the Greatest Common Factor of 54589 and 54600?

Greatest common factor (GCF) of 54589 and 54600 is 1.

GCF(54589,54600) = 1

We will now calculate the prime factors of 54589 and 54600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54589 and 54600.

How to find the GCF of 54589 and 54600?

We will first find the prime factorization of 54589 and 54600. After we will calculate the factors of 54589 and 54600 and find the biggest common factor number .

Step-1: Prime Factorization of 54589

Prime factors of 54589 are 79, 691. Prime factorization of 54589 in exponential form is:

54589 = 79¹ × 691¹

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 54589

List of positive integer factors of 54589 that divides 54589 without a remainder.

1, 79, 691

Step-4: Factors of 54600

List of positive integer factors of 54600 that divides 54589 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 54589 and 54600. The biggest common factor number is the GCF number.
So the greatest common factor 54589 and 54600 is 1.

Also check out the Least Common Multiple of 54589 and 54600