What is the Greatest Common Factor of 17985 and 17996?

Greatest common factor (GCF) of 17985 and 17996 is 11.

GCF(17985,17996) = 11

We will now calculate the prime factors of 17985 and 17996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17985 and 17996.

How to find the GCF of 17985 and 17996?

We will first find the prime factorization of 17985 and 17996. After we will calculate the factors of 17985 and 17996 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 17996

Prime factors of 17996 are 2, 11, 409. Prime factorization of 17996 in exponential form is:

17996 = 2² × 11¹ × 409¹

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 17996

List of positive integer factors of 17996 that divides 17985 without a remainder.

1, 2, 4, 11, 22, 44, 409, 818, 1636, 4499, 8998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17985 and 17996. The biggest common factor number is the GCF number.
So the greatest common factor 17985 and 17996 is 11.

Also check out the Least Common Multiple of 17985 and 17996