What is the Greatest Common Factor of 54945 and 54960?

Greatest common factor (GCF) of 54945 and 54960 is 15.

GCF(54945,54960) = 15

We will now calculate the prime factors of 54945 and 54960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54945 and 54960.

How to find the GCF of 54945 and 54960?

We will first find the prime factorization of 54945 and 54960. After we will calculate the factors of 54945 and 54960 and find the biggest common factor number .

Step-1: Prime Factorization of 54945

Prime factors of 54945 are 3, 5, 11, 37. Prime factorization of 54945 in exponential form is:

54945 = 3³ × 5¹ × 11¹ × 37¹

Step-2: Prime Factorization of 54960

Prime factors of 54960 are 2, 3, 5, 229. Prime factorization of 54960 in exponential form is:

54960 = 2⁴ × 3¹ × 5¹ × 229¹

Step-3: Factors of 54945

List of positive integer factors of 54945 that divides 54945 without a remainder.

1, 3, 5, 9, 11, 15, 27, 33, 37, 45, 55, 99, 111, 135, 165, 185, 297, 333, 407, 495, 555, 999, 1221, 1485, 1665, 2035, 3663, 4995, 6105, 10989, 18315

Step-4: Factors of 54960

List of positive integer factors of 54960 that divides 54945 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 229, 240, 458, 687, 916, 1145, 1374, 1832, 2290, 2748, 3435, 3664, 4580, 5496, 6870, 9160, 10992, 13740, 18320, 27480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54945 and 54960. The biggest common factor number is the GCF number.
So the greatest common factor 54945 and 54960 is 15.

Also check out the Least Common Multiple of 54945 and 54960