What is the Greatest Common Factor of 18000 and 18005?

Greatest common factor (GCF) of 18000 and 18005 is 5.

GCF(18000,18005) = 5

We will now calculate the prime factors of 18000 and 18005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18000 and 18005.

How to find the GCF of 18000 and 18005?

We will first find the prime factorization of 18000 and 18005. After we will calculate the factors of 18000 and 18005 and find the biggest common factor number .

Step-1: Prime Factorization of 18000

Prime factors of 18000 are 2, 3, 5. Prime factorization of 18000 in exponential form is:

18000 = 2⁴ × 3² × 5³

Step-2: Prime Factorization of 18005

Prime factors of 18005 are 5, 13, 277. Prime factorization of 18005 in exponential form is:

18005 = 5¹ × 13¹ × 277¹

Step-3: Factors of 18000

List of positive integer factors of 18000 that divides 18000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 125, 144, 150, 180, 200, 225, 240, 250, 300, 360, 375, 400, 450, 500, 600, 720, 750, 900, 1000, 1125, 1200, 1500, 1800, 2000, 2250, 3000, 3600, 4500, 6000, 9000

Step-4: Factors of 18005

List of positive integer factors of 18005 that divides 18000 without a remainder.

1, 5, 13, 65, 277, 1385, 3601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18000 and 18005. The biggest common factor number is the GCF number.
So the greatest common factor 18000 and 18005 is 5.

Also check out the Least Common Multiple of 18000 and 18005