What is the Greatest Common Factor of 34188 and 34199?

Greatest common factor (GCF) of 34188 and 34199 is 11.

GCF(34188,34199) = 11

We will now calculate the prime factors of 34188 and 34199, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34188 and 34199.

How to find the GCF of 34188 and 34199?

We will first find the prime factorization of 34188 and 34199. After we will calculate the factors of 34188 and 34199 and find the biggest common factor number .

Step-1: Prime Factorization of 34188

Prime factors of 34188 are 2, 3, 7, 11, 37. Prime factorization of 34188 in exponential form is:

34188 = 2² × 3¹ × 7¹ × 11¹ × 37¹

Step-2: Prime Factorization of 34199

Prime factors of 34199 are 11, 3109. Prime factorization of 34199 in exponential form is:

34199 = 11¹ × 3109¹

Step-3: Factors of 34188

List of positive integer factors of 34188 that divides 34188 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 37, 42, 44, 66, 74, 77, 84, 111, 132, 148, 154, 222, 231, 259, 308, 407, 444, 462, 518, 777, 814, 924, 1036, 1221, 1554, 1628, 2442, 2849, 3108, 4884, 5698, 8547, 11396, 17094

Step-4: Factors of 34199

List of positive integer factors of 34199 that divides 34188 without a remainder.

1, 11, 3109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34188 and 34199. The biggest common factor number is the GCF number.
So the greatest common factor 34188 and 34199 is 11.

Also check out the Least Common Multiple of 34188 and 34199