What is the Greatest Common Factor of 54000 and 54019?

Greatest common factor (GCF) of 54000 and 54019 is 1.

GCF(54000,54019) = 1

We will now calculate the prime factors of 54000 and 54019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54000 and 54019.

How to find the GCF of 54000 and 54019?

We will first find the prime factorization of 54000 and 54019. After we will calculate the factors of 54000 and 54019 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 54019

Prime factors of 54019 are 7, 7717. Prime factorization of 54019 in exponential form is:

54019 = 7¹ × 7717¹

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 54019

List of positive integer factors of 54019 that divides 54000 without a remainder.

1, 7, 7717

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54000 and 54019. The biggest common factor number is the GCF number.
So the greatest common factor 54000 and 54019 is 1.

Also check out the Least Common Multiple of 54000 and 54019