What is the Greatest Common Factor of 54960 and 54975?

Greatest common factor (GCF) of 54960 and 54975 is 15.

GCF(54960,54975) = 15

We will now calculate the prime factors of 54960 and 54975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54960 and 54975.

How to find the GCF of 54960 and 54975?

We will first find the prime factorization of 54960 and 54975. After we will calculate the factors of 54960 and 54975 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54975

Prime factors of 54975 are 3, 5, 733. Prime factorization of 54975 in exponential form is:

54975 = 3¹ × 5² × 733¹

Step-3: Factors of 54960

List of positive integer factors of 54960 that divides 54960 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

Step-4: Factors of 54975

List of positive integer factors of 54975 that divides 54960 without a remainder.

1, 3, 5, 15, 25, 75, 733, 2199, 3665, 10995, 18325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54960 and 54975. The biggest common factor number is the GCF number.
So the greatest common factor 54960 and 54975 is 15.

Also check out the Least Common Multiple of 54960 and 54975