What is the Greatest Common Factor of 34004 and 34017?

Greatest common factor (GCF) of 34004 and 34017 is 1.

GCF(34004,34017) = 1

We will now calculate the prime factors of 34004 and 34017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34004 and 34017.

How to find the GCF of 34004 and 34017?

We will first find the prime factorization of 34004 and 34017. After we will calculate the factors of 34004 and 34017 and find the biggest common factor number .

Step-1: Prime Factorization of 34004

Prime factors of 34004 are 2, 8501. Prime factorization of 34004 in exponential form is:

34004 = 2² × 8501¹

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 34004

List of positive integer factors of 34004 that divides 34004 without a remainder.

1, 2, 4, 8501, 17002

Step-4: Factors of 34017

List of positive integer factors of 34017 that divides 34004 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 34004 and 34017. The biggest common factor number is the GCF number.
So the greatest common factor 34004 and 34017 is 1.

Also check out the Least Common Multiple of 34004 and 34017