What is the Greatest Common Factor of 34004 and 34010?

Greatest common factor (GCF) of 34004 and 34010 is 2.

GCF(34004,34010) = 2

We will now calculate the prime factors of 34004 and 34010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34004 and 34010.

How to find the GCF of 34004 and 34010?

We will first find the prime factorization of 34004 and 34010. After we will calculate the factors of 34004 and 34010 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 34010

Prime factors of 34010 are 2, 5, 19, 179. Prime factorization of 34010 in exponential form is:

34010 = 2¹ × 5¹ × 19¹ × 179¹

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 34010

List of positive integer factors of 34010 that divides 34004 without a remainder.

1, 2, 5, 10, 19, 38, 95, 179, 190, 358, 895, 1790, 3401, 6802, 17005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34004 and 34010. The biggest common factor number is the GCF number.
So the greatest common factor 34004 and 34010 is 2.

Also check out the Least Common Multiple of 34004 and 34010