What is the Greatest Common Factor of 34192 and 34208?

Greatest common factor (GCF) of 34192 and 34208 is 16.

GCF(34192,34208) = 16

We will now calculate the prime factors of 34192 and 34208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34192 and 34208.

How to find the GCF of 34192 and 34208?

We will first find the prime factorization of 34192 and 34208. After we will calculate the factors of 34192 and 34208 and find the biggest common factor number .

Step-1: Prime Factorization of 34192

Prime factors of 34192 are 2, 2137. Prime factorization of 34192 in exponential form is:

34192 = 2⁴ × 2137¹

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 34192

List of positive integer factors of 34192 that divides 34192 without a remainder.

1, 2, 4, 8, 16, 2137, 4274, 8548, 17096

Step-4: Factors of 34208

List of positive integer factors of 34208 that divides 34192 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 34192 and 34208. The biggest common factor number is the GCF number.
So the greatest common factor 34192 and 34208 is 16.

Also check out the Least Common Multiple of 34192 and 34208