What is the Greatest Common Factor of 27000 and 27015?

Greatest common factor (GCF) of 27000 and 27015 is 15.

GCF(27000,27015) = 15

We will now calculate the prime factors of 27000 and 27015, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27000 and 27015.

How to find the GCF of 27000 and 27015?

We will first find the prime factorization of 27000 and 27015. After we will calculate the factors of 27000 and 27015 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 27015

Prime factors of 27015 are 3, 5, 1801. Prime factorization of 27015 in exponential form is:

27015 = 3¹ × 5¹ × 1801¹

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 27015

List of positive integer factors of 27015 that divides 27000 without a remainder.

1, 3, 5, 15, 1801, 5403, 9005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27000 and 27015. The biggest common factor number is the GCF number.
So the greatest common factor 27000 and 27015 is 15.

Also check out the Least Common Multiple of 27000 and 27015