What is the Greatest Common Factor of 14175 and 14189?

Greatest common factor (GCF) of 14175 and 14189 is 7.

GCF(14175,14189) = 7

We will now calculate the prime factors of 14175 and 14189, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14175 and 14189.

How to find the GCF of 14175 and 14189?

We will first find the prime factorization of 14175 and 14189. After we will calculate the factors of 14175 and 14189 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 14189

Prime factors of 14189 are 7, 2027. Prime factorization of 14189 in exponential form is:

14189 = 7¹ × 2027¹

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 14189

List of positive integer factors of 14189 that divides 14175 without a remainder.

1, 7, 2027

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14175 and 14189. The biggest common factor number is the GCF number.
So the greatest common factor 14175 and 14189 is 7.

Also check out the Least Common Multiple of 14175 and 14189