What is the Greatest Common Factor of 17000 and 17005?

Greatest common factor (GCF) of 17000 and 17005 is 5.

GCF(17000,17005) = 5

We will now calculate the prime factors of 17000 and 17005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17000 and 17005.

How to find the GCF of 17000 and 17005?

We will first find the prime factorization of 17000 and 17005. After we will calculate the factors of 17000 and 17005 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 17005

Prime factors of 17005 are 5, 19, 179. Prime factorization of 17005 in exponential form is:

17005 = 5¹ × 19¹ × 179¹

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 17005

List of positive integer factors of 17005 that divides 17000 without a remainder.

1, 5, 19, 95, 179, 895, 3401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17000 and 17005. The biggest common factor number is the GCF number.
So the greatest common factor 17000 and 17005 is 5.

Also check out the Least Common Multiple of 17000 and 17005