What is the Greatest Common Factor of 34000 and 34017?

Greatest common factor (GCF) of 34000 and 34017 is 17.

GCF(34000,34017) = 17

We will now calculate the prime factors of 34000 and 34017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34000 and 34017.

How to find the GCF of 34000 and 34017?

We will first find the prime factorization of 34000 and 34017. After we will calculate the factors of 34000 and 34017 and find the biggest common factor number .

Step-1: Prime Factorization of 34000

Prime factors of 34000 are 2, 5, 17. Prime factorization of 34000 in exponential form is:

34000 = 2⁴ × 5³ × 17¹

Step-2: Prime Factorization of 34017

Prime factors of 34017 are 3, 17, 23, 29. Prime factorization of 34017 in exponential form is:

34017 = 3¹ × 17¹ × 23¹ × 29¹

Step-3: Factors of 34000

List of positive integer factors of 34000 that divides 34000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000

Step-4: Factors of 34017

List of positive integer factors of 34017 that divides 34000 without a remainder.

1, 3, 17, 23, 29, 51, 69, 87, 391, 493, 667, 1173, 1479, 2001, 11339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34000 and 34017. The biggest common factor number is the GCF number.
So the greatest common factor 34000 and 34017 is 17.

Also check out the Least Common Multiple of 34000 and 34017