What is the Greatest Common Factor of 27000 and 27004?

Greatest common factor (GCF) of 27000 and 27004 is 4.

GCF(27000,27004) = 4

We will now calculate the prime factors of 27000 and 27004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27000 and 27004.

How to find the GCF of 27000 and 27004?

We will first find the prime factorization of 27000 and 27004. After we will calculate the factors of 27000 and 27004 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 27004

Prime factors of 27004 are 2, 43, 157. Prime factorization of 27004 in exponential form is:

27004 = 2² × 43¹ × 157¹

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 27004

List of positive integer factors of 27004 that divides 27000 without a remainder.

1, 2, 4, 43, 86, 157, 172, 314, 628, 6751, 13502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27000 and 27004. The biggest common factor number is the GCF number.
So the greatest common factor 27000 and 27004 is 4.

Also check out the Least Common Multiple of 27000 and 27004