What is the Greatest Common Factor of 14540 and 14560?

Greatest common factor (GCF) of 14540 and 14560 is 20.

GCF(14540,14560) = 20

We will now calculate the prime factors of 14540 and 14560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14540 and 14560.

How to find the GCF of 14540 and 14560?

We will first find the prime factorization of 14540 and 14560. After we will calculate the factors of 14540 and 14560 and find the biggest common factor number .

Step-1: Prime Factorization of 14540

Prime factors of 14540 are 2, 5, 727. Prime factorization of 14540 in exponential form is:

14540 = 2² × 5¹ × 727¹

Step-2: 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-3: Factors of 14540

List of positive integer factors of 14540 that divides 14540 without a remainder.

1, 2, 4, 5, 10, 20, 727, 1454, 2908, 3635, 7270

Step-4: Factors of 14560

List of positive integer factors of 14560 that divides 14540 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14540 and 14560. The biggest common factor number is the GCF number.
So the greatest common factor 14540 and 14560 is 20.

Also check out the Least Common Multiple of 14540 and 14560