What is the Greatest Common Factor of 54375 and 54384?

Greatest common factor (GCF) of 54375 and 54384 is 3.

GCF(54375,54384) = 3

We will now calculate the prime factors of 54375 and 54384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54375 and 54384.

How to find the GCF of 54375 and 54384?

We will first find the prime factorization of 54375 and 54384. After we will calculate the factors of 54375 and 54384 and find the biggest common factor number .

Step-1: Prime Factorization of 54375

Prime factors of 54375 are 3, 5, 29. Prime factorization of 54375 in exponential form is:

54375 = 3¹ × 5⁴ × 29¹

Step-2: Prime Factorization of 54384

Prime factors of 54384 are 2, 3, 11, 103. Prime factorization of 54384 in exponential form is:

54384 = 2⁴ × 3¹ × 11¹ × 103¹

Step-3: Factors of 54375

List of positive integer factors of 54375 that divides 54375 without a remainder.

1, 3, 5, 15, 25, 29, 75, 87, 125, 145, 375, 435, 625, 725, 1875, 2175, 3625, 10875, 18125

Step-4: Factors of 54384

List of positive integer factors of 54384 that divides 54375 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 103, 132, 176, 206, 264, 309, 412, 528, 618, 824, 1133, 1236, 1648, 2266, 2472, 3399, 4532, 4944, 6798, 9064, 13596, 18128, 27192

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54375 and 54384. The biggest common factor number is the GCF number.
So the greatest common factor 54375 and 54384 is 3.

Also check out the Least Common Multiple of 54375 and 54384