What is the Greatest Common Factor of 17985 and 18005?

Greatest common factor (GCF) of 17985 and 18005 is 5.

GCF(17985,18005) = 5

We will now calculate the prime factors of 17985 and 18005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17985 and 18005.

How to find the GCF of 17985 and 18005?

We will first find the prime factorization of 17985 and 18005. After we will calculate the factors of 17985 and 18005 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 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 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 18005

List of positive integer factors of 18005 that divides 17985 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17985 and 18005. The biggest common factor number is the GCF number.
So the greatest common factor 17985 and 18005 is 5.

Also check out the Least Common Multiple of 17985 and 18005