What is the Greatest Common Factor of 54369 and 54384?

Greatest common factor (GCF) of 54369 and 54384 is 3.

GCF(54369,54384) = 3

We will now calculate the prime factors of 54369 and 54384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54369 and 54384.

How to find the GCF of 54369 and 54384?

We will first find the prime factorization of 54369 and 54384. After we will calculate the factors of 54369 and 54384 and find the biggest common factor number .

Step-1: Prime Factorization of 54369

Prime factors of 54369 are 3, 7, 863. Prime factorization of 54369 in exponential form is:

54369 = 3² × 7¹ × 863¹

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 54369

List of positive integer factors of 54369 that divides 54369 without a remainder.

1, 3, 7, 9, 21, 63, 863, 2589, 6041, 7767, 18123

Step-4: Factors of 54384

List of positive integer factors of 54384 that divides 54369 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 54369 and 54384. The biggest common factor number is the GCF number.
So the greatest common factor 54369 and 54384 is 3.

Also check out the Least Common Multiple of 54369 and 54384