What is the Greatest Common Factor of 34125 and 34134?

Greatest common factor (GCF) of 34125 and 34134 is 3.

GCF(34125,34134) = 3

We will now calculate the prime factors of 34125 and 34134, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34125 and 34134.

How to find the GCF of 34125 and 34134?

We will first find the prime factorization of 34125 and 34134. After we will calculate the factors of 34125 and 34134 and find the biggest common factor number .

Step-1: Prime Factorization of 34125

Prime factors of 34125 are 3, 5, 7, 13. Prime factorization of 34125 in exponential form is:

34125 = 3¹ × 5³ × 7¹ × 13¹

Step-2: Prime Factorization of 34134

Prime factors of 34134 are 2, 3, 5689. Prime factorization of 34134 in exponential form is:

34134 = 2¹ × 3¹ × 5689¹

Step-3: Factors of 34125

List of positive integer factors of 34125 that divides 34125 without a remainder.

1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 125, 175, 195, 273, 325, 375, 455, 525, 875, 975, 1365, 1625, 2275, 2625, 4875, 6825, 11375

Step-4: Factors of 34134

List of positive integer factors of 34134 that divides 34125 without a remainder.

1, 2, 3, 6, 5689, 11378, 17067

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34125 and 34134. The biggest common factor number is the GCF number.
So the greatest common factor 34125 and 34134 is 3.

Also check out the Least Common Multiple of 34125 and 34134