What is the Greatest Common Factor of 17000 and 17009?

Greatest common factor (GCF) of 17000 and 17009 is 1.

GCF(17000,17009) = 1

We will now calculate the prime factors of 17000 and 17009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17000 and 17009.

How to find the GCF of 17000 and 17009?

We will first find the prime factorization of 17000 and 17009. After we will calculate the factors of 17000 and 17009 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17009

Prime factors of 17009 are 73, 233. Prime factorization of 17009 in exponential form is:

17009 = 73¹ × 233¹

Step-3: Factors of 17000

List of positive integer factors of 17000 that divides 17000 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

Step-4: Factors of 17009

List of positive integer factors of 17009 that divides 17000 without a remainder.

1, 73, 233

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17000 and 17009. The biggest common factor number is the GCF number.
So the greatest common factor 17000 and 17009 is 1.

Also check out the Least Common Multiple of 17000 and 17009