What is the Greatest Common Factor of 14560 and 14567?

Greatest common factor (GCF) of 14560 and 14567 is 7.

GCF(14560,14567) = 7

We will now calculate the prime factors of 14560 and 14567, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14560 and 14567.

How to find the GCF of 14560 and 14567?

We will first find the prime factorization of 14560 and 14567. After we will calculate the factors of 14560 and 14567 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 14567

Prime factors of 14567 are 7, 2081. Prime factorization of 14567 in exponential form is:

14567 = 7¹ × 2081¹

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 14567

List of positive integer factors of 14567 that divides 14560 without a remainder.

1, 7, 2081

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14560 and 14567. The biggest common factor number is the GCF number.
So the greatest common factor 14560 and 14567 is 7.

Also check out the Least Common Multiple of 14560 and 14567