What is the Greatest Common Factor of 14160 and 14175?

Greatest common factor (GCF) of 14160 and 14175 is 15.

GCF(14160,14175) = 15

We will now calculate the prime factors of 14160 and 14175, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14160 and 14175.

How to find the GCF of 14160 and 14175?

We will first find the prime factorization of 14160 and 14175. After we will calculate the factors of 14160 and 14175 and find the biggest common factor number .

Step-1: Prime Factorization of 14160

Prime factors of 14160 are 2, 3, 5, 59. Prime factorization of 14160 in exponential form is:

14160 = 2⁴ × 3¹ × 5¹ × 59¹

Step-2: 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-3: Factors of 14160

List of positive integer factors of 14160 that divides 14160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 59, 60, 80, 118, 120, 177, 236, 240, 295, 354, 472, 590, 708, 885, 944, 1180, 1416, 1770, 2360, 2832, 3540, 4720, 7080

Step-4: Factors of 14175

List of positive integer factors of 14175 that divides 14160 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14160 and 14175. The biggest common factor number is the GCF number.
So the greatest common factor 14160 and 14175 is 15.

Also check out the Least Common Multiple of 14160 and 14175