What is the Greatest Common Factor of 17985 and 18000?

Greatest common factor (GCF) of 17985 and 18000 is 15.

GCF(17985,18000) = 15

We will now calculate the prime factors of 17985 and 18000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17985 and 18000.

How to find the GCF of 17985 and 18000?

We will first find the prime factorization of 17985 and 18000. After we will calculate the factors of 17985 and 18000 and find the biggest common factor number .

Step-1: Prime Factorization of 17985

Prime factors of 17985 are 3, 5, 11, 109. Prime factorization of 17985 in exponential form is:

17985 = 3¹ × 5¹ × 11¹ × 109¹

Step-2: 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-3: Factors of 17985

List of positive integer factors of 17985 that divides 17985 without a remainder.

1, 3, 5, 11, 15, 33, 55, 109, 165, 327, 545, 1199, 1635, 3597, 5995

Step-4: Factors of 18000

List of positive integer factors of 18000 that divides 17985 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17985 and 18000. The biggest common factor number is the GCF number.
So the greatest common factor 17985 and 18000 is 15.

Also check out the Least Common Multiple of 17985 and 18000