What is the Greatest Common Factor of 54375 and 54390?

Greatest common factor (GCF) of 54375 and 54390 is 15.

GCF(54375,54390) = 15

We will now calculate the prime factors of 54375 and 54390, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54375 and 54390.

How to find the GCF of 54375 and 54390?

We will first find the prime factorization of 54375 and 54390. After we will calculate the factors of 54375 and 54390 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 54390

Prime factors of 54390 are 2, 3, 5, 7, 37. Prime factorization of 54390 in exponential form is:

54390 = 2¹ × 3¹ × 5¹ × 7² × 37¹

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 54390

List of positive integer factors of 54390 that divides 54375 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 37, 42, 49, 70, 74, 98, 105, 111, 147, 185, 210, 222, 245, 259, 294, 370, 490, 518, 555, 735, 777, 1110, 1295, 1470, 1554, 1813, 2590, 3626, 3885, 5439, 7770, 9065, 10878, 18130, 27195

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54375 and 54390. The biggest common factor number is the GCF number.
So the greatest common factor 54375 and 54390 is 15.

Also check out the Least Common Multiple of 54375 and 54390