What is the Greatest Common Factor of 18000 and 18017?

Greatest common factor (GCF) of 18000 and 18017 is 1.

GCF(18000,18017) = 1

We will now calculate the prime factors of 18000 and 18017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18000 and 18017.

How to find the GCF of 18000 and 18017?

We will first find the prime factorization of 18000 and 18017. After we will calculate the factors of 18000 and 18017 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 18017

Prime factors of 18017 are 43, 419. Prime factorization of 18017 in exponential form is:

18017 = 43¹ × 419¹

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 18017

List of positive integer factors of 18017 that divides 18000 without a remainder.

1, 43, 419

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18000 and 18017. The biggest common factor number is the GCF number.
So the greatest common factor 18000 and 18017 is 1.

Also check out the Least Common Multiple of 18000 and 18017