What is the Greatest Common Factor of 16983 and 17000?

Greatest common factor (GCF) of 16983 and 17000 is 17.

GCF(16983,17000) = 17

We will now calculate the prime factors of 16983 and 17000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16983 and 17000.

How to find the GCF of 16983 and 17000?

We will first find the prime factorization of 16983 and 17000. After we will calculate the factors of 16983 and 17000 and find the biggest common factor number .

Step-1: Prime Factorization of 16983

Prime factors of 16983 are 3, 17, 37. Prime factorization of 16983 in exponential form is:

16983 = 3³ × 17¹ × 37¹

Step-2: Prime Factorization of 17000

Prime factors of 17000 are 2, 5, 17. Prime factorization of 17000 in exponential form is:

17000 = 2³ × 5³ × 17¹

Step-3: Factors of 16983

List of positive integer factors of 16983 that divides 16983 without a remainder.

1, 3, 9, 17, 27, 37, 51, 111, 153, 333, 459, 629, 999, 1887, 5661

Step-4: Factors of 17000

List of positive integer factors of 17000 that divides 16983 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16983 and 17000. The biggest common factor number is the GCF number.
So the greatest common factor 16983 and 17000 is 17.

Also check out the Least Common Multiple of 16983 and 17000