What is the Greatest Common Factor of 54100 and 54120?

Greatest common factor (GCF) of 54100 and 54120 is 20.

GCF(54100,54120) = 20

We will now calculate the prime factors of 54100 and 54120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54100 and 54120.

How to find the GCF of 54100 and 54120?

We will first find the prime factorization of 54100 and 54120. After we will calculate the factors of 54100 and 54120 and find the biggest common factor number .

Step-1: Prime Factorization of 54100

Prime factors of 54100 are 2, 5, 541. Prime factorization of 54100 in exponential form is:

54100 = 2² × 5² × 541¹

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 54100

List of positive integer factors of 54100 that divides 54100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 541, 1082, 2164, 2705, 5410, 10820, 13525, 27050

Step-4: Factors of 54120

List of positive integer factors of 54120 that divides 54100 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 54100 and 54120. The biggest common factor number is the GCF number.
So the greatest common factor 54100 and 54120 is 20.

Also check out the Least Common Multiple of 54100 and 54120