What is the Greatest Common Factor of 14560 and 14575?

Greatest common factor (GCF) of 14560 and 14575 is 5.

GCF(14560,14575) = 5

We will now calculate the prime factors of 14560 and 14575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14560 and 14575.

How to find the GCF of 14560 and 14575?

We will first find the prime factorization of 14560 and 14575. After we will calculate the factors of 14560 and 14575 and find the biggest common factor number .

Step-1: Prime Factorization of 14560

Prime factors of 14560 are 2, 5, 7, 13. Prime factorization of 14560 in exponential form is:

14560 = 2⁵ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 14575

Prime factors of 14575 are 5, 11, 53. Prime factorization of 14575 in exponential form is:

14575 = 5² × 11¹ × 53¹

Step-3: Factors of 14560

List of positive integer factors of 14560 that divides 14560 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 32, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 160, 182, 208, 224, 260, 280, 364, 416, 455, 520, 560, 728, 910, 1040, 1120, 1456, 1820, 2080, 2912, 3640, 7280

Step-4: Factors of 14575

List of positive integer factors of 14575 that divides 14560 without a remainder.

1, 5, 11, 25, 53, 55, 265, 275, 583, 1325, 2915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14560 and 14575. The biggest common factor number is the GCF number.
So the greatest common factor 14560 and 14575 is 5.

Also check out the Least Common Multiple of 14560 and 14575