What is the Greatest Common Factor of 34198 and 34208?

Greatest common factor (GCF) of 34198 and 34208 is 2.

GCF(34198,34208) = 2

We will now calculate the prime factors of 34198 and 34208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34198 and 34208.

How to find the GCF of 34198 and 34208?

We will first find the prime factorization of 34198 and 34208. After we will calculate the factors of 34198 and 34208 and find the biggest common factor number .

Step-1: Prime Factorization of 34198

Prime factors of 34198 are 2, 17099. Prime factorization of 34198 in exponential form is:

34198 = 2¹ × 17099¹

Step-2: Prime Factorization of 34208

Prime factors of 34208 are 2, 1069. Prime factorization of 34208 in exponential form is:

34208 = 2⁵ × 1069¹

Step-3: Factors of 34198

List of positive integer factors of 34198 that divides 34198 without a remainder.

1, 2, 17099

Step-4: Factors of 34208

List of positive integer factors of 34208 that divides 34198 without a remainder.

1, 2, 4, 8, 16, 32, 1069, 2138, 4276, 8552, 17104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34198 and 34208. The biggest common factor number is the GCF number.
So the greatest common factor 34198 and 34208 is 2.

Also check out the Least Common Multiple of 34198 and 34208