What is the Greatest Common Factor of 34176 and 34185?

Greatest common factor (GCF) of 34176 and 34185 is 3.

GCF(34176,34185) = 3

We will now calculate the prime factors of 34176 and 34185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34176 and 34185.

How to find the GCF of 34176 and 34185?

We will first find the prime factorization of 34176 and 34185. After we will calculate the factors of 34176 and 34185 and find the biggest common factor number .

Step-1: Prime Factorization of 34176

Prime factors of 34176 are 2, 3, 89. Prime factorization of 34176 in exponential form is:

34176 = 2⁷ × 3¹ × 89¹

Step-2: Prime Factorization of 34185

Prime factors of 34185 are 3, 5, 43, 53. Prime factorization of 34185 in exponential form is:

34185 = 3¹ × 5¹ × 43¹ × 53¹

Step-3: Factors of 34176

List of positive integer factors of 34176 that divides 34176 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 89, 96, 128, 178, 192, 267, 356, 384, 534, 712, 1068, 1424, 2136, 2848, 4272, 5696, 8544, 11392, 17088

Step-4: Factors of 34185

List of positive integer factors of 34185 that divides 34176 without a remainder.

1, 3, 5, 15, 43, 53, 129, 159, 215, 265, 645, 795, 2279, 6837, 11395

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34176 and 34185. The biggest common factor number is the GCF number.
So the greatest common factor 34176 and 34185 is 3.

Also check out the Least Common Multiple of 34176 and 34185