What is the Greatest Common Factor of 54600 and 54614?

Greatest common factor (GCF) of 54600 and 54614 is 14.

GCF(54600,54614) = 14

We will now calculate the prime factors of 54600 and 54614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54600 and 54614.

How to find the GCF of 54600 and 54614?

We will first find the prime factorization of 54600 and 54614. After we will calculate the factors of 54600 and 54614 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 54614

Prime factors of 54614 are 2, 7, 47, 83. Prime factorization of 54614 in exponential form is:

54614 = 2¹ × 7¹ × 47¹ × 83¹

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 54614

List of positive integer factors of 54614 that divides 54600 without a remainder.

1, 2, 7, 14, 47, 83, 94, 166, 329, 581, 658, 1162, 3901, 7802, 27307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54600 and 54614. The biggest common factor number is the GCF number.
So the greatest common factor 54600 and 54614 is 14.

Also check out the Least Common Multiple of 54600 and 54614