What is the Greatest Common Factor of 14560 and 14564?

Greatest common factor (GCF) of 14560 and 14564 is 4.

GCF(14560,14564) = 4

We will now calculate the prime factors of 14560 and 14564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14560 and 14564.

How to find the GCF of 14560 and 14564?

We will first find the prime factorization of 14560 and 14564. After we will calculate the factors of 14560 and 14564 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 14564

Prime factors of 14564 are 2, 11, 331. Prime factorization of 14564 in exponential form is:

14564 = 2² × 11¹ × 331¹

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 14564

List of positive integer factors of 14564 that divides 14560 without a remainder.

1, 2, 4, 11, 22, 44, 331, 662, 1324, 3641, 7282

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14560 and 14564. The biggest common factor number is the GCF number.
So the greatest common factor 14560 and 14564 is 4.

Also check out the Least Common Multiple of 14560 and 14564