What is the Greatest Common Factor of 27000 and 27019?

Greatest common factor (GCF) of 27000 and 27019 is 1.

GCF(27000,27019) = 1

We will now calculate the prime factors of 27000 and 27019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27000 and 27019.

How to find the GCF of 27000 and 27019?

We will first find the prime factorization of 27000 and 27019. After we will calculate the factors of 27000 and 27019 and find the biggest common factor number .

Step-1: Prime Factorization of 27000

Prime factors of 27000 are 2, 3, 5. Prime factorization of 27000 in exponential form is:

27000 = 2³ × 3³ × 5³

Step-2: Prime Factorization of 27019

Prime factors of 27019 are 41, 659. Prime factorization of 27019 in exponential form is:

27019 = 41¹ × 659¹

Step-3: Factors of 27000

List of positive integer factors of 27000 that divides 27000 without a remainder.

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

Step-4: Factors of 27019

List of positive integer factors of 27019 that divides 27000 without a remainder.

1, 41, 659

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27000 and 27019. The biggest common factor number is the GCF number.
So the greatest common factor 27000 and 27019 is 1.

Also check out the Least Common Multiple of 27000 and 27019