What is the Greatest Common Factor of 14175 and 14184?

Greatest common factor (GCF) of 14175 and 14184 is 9.

GCF(14175,14184) = 9

We will now calculate the prime factors of 14175 and 14184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14175 and 14184.

How to find the GCF of 14175 and 14184?

We will first find the prime factorization of 14175 and 14184. After we will calculate the factors of 14175 and 14184 and find the biggest common factor number .

Step-1: Prime Factorization of 14175

Prime factors of 14175 are 3, 5, 7. Prime factorization of 14175 in exponential form is:

14175 = 3⁴ × 5² × 7¹

Step-2: Prime Factorization of 14184

Prime factors of 14184 are 2, 3, 197. Prime factorization of 14184 in exponential form is:

14184 = 2³ × 3² × 197¹

Step-3: Factors of 14175

List of positive integer factors of 14175 that divides 14175 without a remainder.

1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 81, 105, 135, 175, 189, 225, 315, 405, 525, 567, 675, 945, 1575, 2025, 2835, 4725

Step-4: Factors of 14184

List of positive integer factors of 14184 that divides 14175 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 197, 394, 591, 788, 1182, 1576, 1773, 2364, 3546, 4728, 7092

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14175 and 14184. The biggest common factor number is the GCF number.
So the greatest common factor 14175 and 14184 is 9.

Also check out the Least Common Multiple of 14175 and 14184