What is the Greatest Common Factor of 54000 and 54005?

Greatest common factor (GCF) of 54000 and 54005 is 5.

GCF(54000,54005) = 5

We will now calculate the prime factors of 54000 and 54005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54000 and 54005.

How to find the GCF of 54000 and 54005?

We will first find the prime factorization of 54000 and 54005. After we will calculate the factors of 54000 and 54005 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 54005

Prime factors of 54005 are 5, 7, 1543. Prime factorization of 54005 in exponential form is:

54005 = 5¹ × 7¹ × 1543¹

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 54005

List of positive integer factors of 54005 that divides 54000 without a remainder.

1, 5, 7, 35, 1543, 7715, 10801

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54000 and 54005. The biggest common factor number is the GCF number.
So the greatest common factor 54000 and 54005 is 5.

Also check out the Least Common Multiple of 54000 and 54005