What is the Greatest Common Factor of 17175 and 17184?

Greatest common factor (GCF) of 17175 and 17184 is 3.

GCF(17175,17184) = 3

We will now calculate the prime factors of 17175 and 17184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17175 and 17184.

How to find the GCF of 17175 and 17184?

We will first find the prime factorization of 17175 and 17184. After we will calculate the factors of 17175 and 17184 and find the biggest common factor number .

Step-1: Prime Factorization of 17175

Prime factors of 17175 are 3, 5, 229. Prime factorization of 17175 in exponential form is:

17175 = 3¹ × 5² × 229¹

Step-2: Prime Factorization of 17184

Prime factors of 17184 are 2, 3, 179. Prime factorization of 17184 in exponential form is:

17184 = 2⁵ × 3¹ × 179¹

Step-3: Factors of 17175

List of positive integer factors of 17175 that divides 17175 without a remainder.

1, 3, 5, 15, 25, 75, 229, 687, 1145, 3435, 5725

Step-4: Factors of 17184

List of positive integer factors of 17184 that divides 17175 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 179, 358, 537, 716, 1074, 1432, 2148, 2864, 4296, 5728, 8592

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17175 and 17184. The biggest common factor number is the GCF number.
So the greatest common factor 17175 and 17184 is 3.

Also check out the Least Common Multiple of 17175 and 17184