What is the Greatest Common Factor of 34125 and 34138?

Greatest common factor (GCF) of 34125 and 34138 is 13.

GCF(34125,34138) = 13

We will now calculate the prime factors of 34125 and 34138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34125 and 34138.

How to find the GCF of 34125 and 34138?

We will first find the prime factorization of 34125 and 34138. After we will calculate the factors of 34125 and 34138 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 34138

Prime factors of 34138 are 2, 13, 101. Prime factorization of 34138 in exponential form is:

34138 = 2¹ × 13² × 101¹

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 34138

List of positive integer factors of 34138 that divides 34125 without a remainder.

1, 2, 13, 26, 101, 169, 202, 338, 1313, 2626, 17069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34125 and 34138. The biggest common factor number is the GCF number.
So the greatest common factor 34125 and 34138 is 13.

Also check out the Least Common Multiple of 34125 and 34138