What is the Greatest Common Factor of 54360 and 54375?

Greatest common factor (GCF) of 54360 and 54375 is 15.

GCF(54360,54375) = 15

We will now calculate the prime factors of 54360 and 54375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54360 and 54375.

How to find the GCF of 54360 and 54375?

We will first find the prime factorization of 54360 and 54375. After we will calculate the factors of 54360 and 54375 and find the biggest common factor number .

Step-1: Prime Factorization of 54360

Prime factors of 54360 are 2, 3, 5, 151. Prime factorization of 54360 in exponential form is:

54360 = 2³ × 3² × 5¹ × 151¹

Step-2: 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-3: Factors of 54360

List of positive integer factors of 54360 that divides 54360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 151, 180, 302, 360, 453, 604, 755, 906, 1208, 1359, 1510, 1812, 2265, 2718, 3020, 3624, 4530, 5436, 6040, 6795, 9060, 10872, 13590, 18120, 27180

Step-4: Factors of 54375

List of positive integer factors of 54375 that divides 54360 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54360 and 54375. The biggest common factor number is the GCF number.
So the greatest common factor 54360 and 54375 is 15.

Also check out the Least Common Multiple of 54360 and 54375