What is the Greatest Common Factor of 17985 and 17991?

Greatest common factor (GCF) of 17985 and 17991 is 3.

GCF(17985,17991) = 3

We will now calculate the prime factors of 17985 and 17991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17985 and 17991.

How to find the GCF of 17985 and 17991?

We will first find the prime factorization of 17985 and 17991. After we will calculate the factors of 17985 and 17991 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 17991

Prime factors of 17991 are 3, 1999. Prime factorization of 17991 in exponential form is:

17991 = 3² × 1999¹

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 17991

List of positive integer factors of 17991 that divides 17985 without a remainder.

1, 3, 9, 1999, 5997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17985 and 17991. The biggest common factor number is the GCF number.
So the greatest common factor 17985 and 17991 is 3.

Also check out the Least Common Multiple of 17985 and 17991