What is the Greatest Common Factor of 54120 and 54138?

Greatest common factor (GCF) of 54120 and 54138 is 6.

GCF(54120,54138) = 6

We will now calculate the prime factors of 54120 and 54138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54120 and 54138.

How to find the GCF of 54120 and 54138?

We will first find the prime factorization of 54120 and 54138. After we will calculate the factors of 54120 and 54138 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54138

Prime factors of 54138 are 2, 3, 7, 1289. Prime factorization of 54138 in exponential form is:

54138 = 2¹ × 3¹ × 7¹ × 1289¹

Step-3: Factors of 54120

List of positive integer factors of 54120 that divides 54120 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

Step-4: Factors of 54138

List of positive integer factors of 54138 that divides 54120 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1289, 2578, 3867, 7734, 9023, 18046, 27069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54120 and 54138. The biggest common factor number is the GCF number.
So the greatest common factor 54120 and 54138 is 6.

Also check out the Least Common Multiple of 54120 and 54138