What is the Greatest Common Factor of 54109 and 54120?

Greatest common factor (GCF) of 54109 and 54120 is 11.

GCF(54109,54120) = 11

We will now calculate the prime factors of 54109 and 54120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54109 and 54120.

How to find the GCF of 54109 and 54120?

We will first find the prime factorization of 54109 and 54120. After we will calculate the factors of 54109 and 54120 and find the biggest common factor number .

Step-1: Prime Factorization of 54109

Prime factors of 54109 are 11, 4919. Prime factorization of 54109 in exponential form is:

54109 = 11¹ × 4919¹

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 54109

List of positive integer factors of 54109 that divides 54109 without a remainder.

1, 11, 4919

Step-4: Factors of 54120

List of positive integer factors of 54120 that divides 54109 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 54109 and 54120. The biggest common factor number is the GCF number.
So the greatest common factor 54109 and 54120 is 11.

Also check out the Least Common Multiple of 54109 and 54120