What is the Greatest Common Factor of 54114 and 54120?

Greatest common factor (GCF) of 54114 and 54120 is 6.

GCF(54114,54120) = 6

We will now calculate the prime factors of 54114 and 54120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54114 and 54120.

How to find the GCF of 54114 and 54120?

We will first find the prime factorization of 54114 and 54120. After we will calculate the factors of 54114 and 54120 and find the biggest common factor number .

Step-1: Prime Factorization of 54114

Prime factors of 54114 are 2, 3, 29, 311. Prime factorization of 54114 in exponential form is:

54114 = 2¹ × 3¹ × 29¹ × 311¹

Step-2: Prime Factorization of 54120

Prime factors of 54120 are 2, 3, 5, 11, 41. Prime factorization of 54120 in exponential form is:

54120 = 2³ × 3¹ × 5¹ × 11¹ × 41¹

Step-3: Factors of 54114

List of positive integer factors of 54114 that divides 54114 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174, 311, 622, 933, 1866, 9019, 18038, 27057

Step-4: Factors of 54120

List of positive integer factors of 54120 that divides 54114 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 41, 44, 55, 60, 66, 82, 88, 110, 120, 123, 132, 164, 165, 205, 220, 246, 264, 328, 330, 410, 440, 451, 492, 615, 660, 820, 902, 984, 1230, 1320, 1353, 1640, 1804, 2255, 2460, 2706, 3608, 4510, 4920, 5412, 6765, 9020, 10824, 13530, 18040, 27060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54114 and 54120. The biggest common factor number is the GCF number.
So the greatest common factor 54114 and 54120 is 6.

Also check out the Least Common Multiple of 54114 and 54120