What is the Greatest Common Factor of 34204 and 34214?

Greatest common factor (GCF) of 34204 and 34214 is 2.

GCF(34204,34214) = 2

We will now calculate the prime factors of 34204 and 34214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34204 and 34214.

How to find the GCF of 34204 and 34214?

We will first find the prime factorization of 34204 and 34214. After we will calculate the factors of 34204 and 34214 and find the biggest common factor number .

Step-1: Prime Factorization of 34204

Prime factors of 34204 are 2, 17, 503. Prime factorization of 34204 in exponential form is:

34204 = 2² × 17¹ × 503¹

Step-2: Prime Factorization of 34214

Prime factors of 34214 are 2, 17107. Prime factorization of 34214 in exponential form is:

34214 = 2¹ × 17107¹

Step-3: Factors of 34204

List of positive integer factors of 34204 that divides 34204 without a remainder.

1, 2, 4, 17, 34, 68, 503, 1006, 2012, 8551, 17102

Step-4: Factors of 34214

List of positive integer factors of 34214 that divides 34204 without a remainder.

1, 2, 17107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34204 and 34214. The biggest common factor number is the GCF number.
So the greatest common factor 34204 and 34214 is 2.

Also check out the Least Common Multiple of 34204 and 34214