What is the Greatest Common Factor of 17966 and 17986?

Greatest common factor (GCF) of 17966 and 17986 is 2.

GCF(17966,17986) = 2

We will now calculate the prime factors of 17966 and 17986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17966 and 17986.

How to find the GCF of 17966 and 17986?

We will first find the prime factorization of 17966 and 17986. After we will calculate the factors of 17966 and 17986 and find the biggest common factor number .

Step-1: Prime Factorization of 17966

Prime factors of 17966 are 2, 13, 691. Prime factorization of 17966 in exponential form is:

17966 = 2¹ × 13¹ × 691¹

Step-2: Prime Factorization of 17986

Prime factors of 17986 are 2, 17, 23. Prime factorization of 17986 in exponential form is:

17986 = 2¹ × 17¹ × 23²

Step-3: Factors of 17966

List of positive integer factors of 17966 that divides 17966 without a remainder.

1, 2, 13, 26, 691, 1382, 8983

Step-4: Factors of 17986

List of positive integer factors of 17986 that divides 17966 without a remainder.

1, 2, 17, 23, 34, 46, 391, 529, 782, 1058, 8993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17966 and 17986. The biggest common factor number is the GCF number.
So the greatest common factor 17966 and 17986 is 2.

Also check out the Least Common Multiple of 17966 and 17986