What is the Greatest Common Factor of 34089 and 34104?

Greatest common factor (GCF) of 34089 and 34104 is 3.

GCF(34089,34104) = 3

We will now calculate the prime factors of 34089 and 34104, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34089 and 34104.

How to find the GCF of 34089 and 34104?

We will first find the prime factorization of 34089 and 34104. After we will calculate the factors of 34089 and 34104 and find the biggest common factor number .

Step-1: Prime Factorization of 34089

Prime factors of 34089 are 3, 11, 1033. Prime factorization of 34089 in exponential form is:

34089 = 3¹ × 11¹ × 1033¹

Step-2: Prime Factorization of 34104

Prime factors of 34104 are 2, 3, 7, 29. Prime factorization of 34104 in exponential form is:

34104 = 2³ × 3¹ × 7² × 29¹

Step-3: Factors of 34089

List of positive integer factors of 34089 that divides 34089 without a remainder.

1, 3, 11, 33, 1033, 3099, 11363

Step-4: Factors of 34104

List of positive integer factors of 34104 that divides 34089 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 29, 42, 49, 56, 58, 84, 87, 98, 116, 147, 168, 174, 196, 203, 232, 294, 348, 392, 406, 588, 609, 696, 812, 1176, 1218, 1421, 1624, 2436, 2842, 4263, 4872, 5684, 8526, 11368, 17052

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34089 and 34104. The biggest common factor number is the GCF number.
So the greatest common factor 34089 and 34104 is 3.

Also check out the Least Common Multiple of 34089 and 34104