What is the Greatest Common Factor of 34175 and 34190?

Greatest common factor (GCF) of 34175 and 34190 is 5.

GCF(34175,34190) = 5

We will now calculate the prime factors of 34175 and 34190, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34175 and 34190.

How to find the GCF of 34175 and 34190?

We will first find the prime factorization of 34175 and 34190. After we will calculate the factors of 34175 and 34190 and find the biggest common factor number .

Step-1: Prime Factorization of 34175

Prime factors of 34175 are 5, 1367. Prime factorization of 34175 in exponential form is:

34175 = 5² × 1367¹

Step-2: Prime Factorization of 34190

Prime factors of 34190 are 2, 5, 13, 263. Prime factorization of 34190 in exponential form is:

34190 = 2¹ × 5¹ × 13¹ × 263¹

Step-3: Factors of 34175

List of positive integer factors of 34175 that divides 34175 without a remainder.

1, 5, 25, 1367, 6835

Step-4: Factors of 34190

List of positive integer factors of 34190 that divides 34175 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 263, 526, 1315, 2630, 3419, 6838, 17095

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34175 and 34190. The biggest common factor number is the GCF number.
So the greatest common factor 34175 and 34190 is 5.

Also check out the Least Common Multiple of 34175 and 34190