What is the Greatest Common Factor of 34174 and 34188?

Greatest common factor (GCF) of 34174 and 34188 is 14.

GCF(34174,34188) = 14

We will now calculate the prime factors of 34174 and 34188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34174 and 34188.

How to find the GCF of 34174 and 34188?

We will first find the prime factorization of 34174 and 34188. After we will calculate the factors of 34174 and 34188 and find the biggest common factor number .

Step-1: Prime Factorization of 34174

Prime factors of 34174 are 2, 7, 2441. Prime factorization of 34174 in exponential form is:

34174 = 2¹ × 7¹ × 2441¹

Step-2: 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-3: Factors of 34174

List of positive integer factors of 34174 that divides 34174 without a remainder.

1, 2, 7, 14, 2441, 4882, 17087

Step-4: Factors of 34188

List of positive integer factors of 34188 that divides 34174 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34174 and 34188. The biggest common factor number is the GCF number.
So the greatest common factor 34174 and 34188 is 14.

Also check out the Least Common Multiple of 34174 and 34188