What is the Greatest Common Factor of 34219 and 34238?

Greatest common factor (GCF) of 34219 and 34238 is 19.

GCF(34219,34238) = 19

We will now calculate the prime factors of 34219 and 34238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34219 and 34238.

How to find the GCF of 34219 and 34238?

We will first find the prime factorization of 34219 and 34238. After we will calculate the factors of 34219 and 34238 and find the biggest common factor number .

Step-1: Prime Factorization of 34219

Prime factors of 34219 are 19, 1801. Prime factorization of 34219 in exponential form is:

34219 = 19¹ × 1801¹

Step-2: Prime Factorization of 34238

Prime factors of 34238 are 2, 17, 19, 53. Prime factorization of 34238 in exponential form is:

34238 = 2¹ × 17¹ × 19¹ × 53¹

Step-3: Factors of 34219

List of positive integer factors of 34219 that divides 34219 without a remainder.

1, 19, 1801

Step-4: Factors of 34238

List of positive integer factors of 34238 that divides 34219 without a remainder.

1, 2, 17, 19, 34, 38, 53, 106, 323, 646, 901, 1007, 1802, 2014, 17119

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34219 and 34238. The biggest common factor number is the GCF number.
So the greatest common factor 34219 and 34238 is 19.

Also check out the Least Common Multiple of 34219 and 34238