What is the Greatest Common Factor of 34195 and 34209?

Greatest common factor (GCF) of 34195 and 34209 is 7.

GCF(34195,34209) = 7

We will now calculate the prime factors of 34195 and 34209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34195 and 34209.

How to find the GCF of 34195 and 34209?

We will first find the prime factorization of 34195 and 34209. After we will calculate the factors of 34195 and 34209 and find the biggest common factor number .

Step-1: Prime Factorization of 34195

Prime factors of 34195 are 5, 7, 977. Prime factorization of 34195 in exponential form is:

34195 = 5¹ × 7¹ × 977¹

Step-2: Prime Factorization of 34209

Prime factors of 34209 are 3, 7, 181. Prime factorization of 34209 in exponential form is:

34209 = 3³ × 7¹ × 181¹

Step-3: Factors of 34195

List of positive integer factors of 34195 that divides 34195 without a remainder.

1, 5, 7, 35, 977, 4885, 6839

Step-4: Factors of 34209

List of positive integer factors of 34209 that divides 34195 without a remainder.

1, 3, 7, 9, 21, 27, 63, 181, 189, 543, 1267, 1629, 3801, 4887, 11403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34195 and 34209. The biggest common factor number is the GCF number.
So the greatest common factor 34195 and 34209 is 7.

Also check out the Least Common Multiple of 34195 and 34209