What is the Greatest Common Factor of 54000 and 54015?

Greatest common factor (GCF) of 54000 and 54015 is 15.

GCF(54000,54015) = 15

We will now calculate the prime factors of 54000 and 54015, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54000 and 54015.

How to find the GCF of 54000 and 54015?

We will first find the prime factorization of 54000 and 54015. After we will calculate the factors of 54000 and 54015 and find the biggest common factor number .

Step-1: Prime Factorization of 54000

Prime factors of 54000 are 2, 3, 5. Prime factorization of 54000 in exponential form is:

54000 = 2⁴ × 3³ × 5³

Step-2: Prime Factorization of 54015

Prime factors of 54015 are 3, 5, 13, 277. Prime factorization of 54015 in exponential form is:

54015 = 3¹ × 5¹ × 13¹ × 277¹

Step-3: Factors of 54000

List of positive integer factors of 54000 that divides 54000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 125, 135, 144, 150, 180, 200, 216, 225, 240, 250, 270, 300, 360, 375, 400, 432, 450, 500, 540, 600, 675, 720, 750, 900, 1000, 1080, 1125, 1200, 1350, 1500, 1800, 2000, 2160, 2250, 2700, 3000, 3375, 3600, 4500, 5400, 6000, 6750, 9000, 10800, 13500, 18000, 27000

Step-4: Factors of 54015

List of positive integer factors of 54015 that divides 54000 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 277, 831, 1385, 3601, 4155, 10803, 18005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54000 and 54015. The biggest common factor number is the GCF number.
So the greatest common factor 54000 and 54015 is 15.

Also check out the Least Common Multiple of 54000 and 54015