What is the Greatest Common Factor of 17986 and 18003?

Greatest common factor (GCF) of 17986 and 18003 is 17.

GCF(17986,18003) = 17

We will now calculate the prime factors of 17986 and 18003, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17986 and 18003.

How to find the GCF of 17986 and 18003?

We will first find the prime factorization of 17986 and 18003. After we will calculate the factors of 17986 and 18003 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 18003

Prime factors of 18003 are 3, 17, 353. Prime factorization of 18003 in exponential form is:

18003 = 3¹ × 17¹ × 353¹

Step-3: Factors of 17986

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

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

Step-4: Factors of 18003

List of positive integer factors of 18003 that divides 17986 without a remainder.

1, 3, 17, 51, 353, 1059, 6001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17986 and 18003. The biggest common factor number is the GCF number.
So the greatest common factor 17986 and 18003 is 17.

Also check out the Least Common Multiple of 17986 and 18003