What is the Greatest Common Factor of 28560 and 28567?

Greatest common factor (GCF) of 28560 and 28567 is 7.

GCF(28560,28567) = 7

We will now calculate the prime factors of 28560 and 28567, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28560 and 28567.

How to find the GCF of 28560 and 28567?

We will first find the prime factorization of 28560 and 28567. After we will calculate the factors of 28560 and 28567 and find the biggest common factor number .

Step-1: Prime Factorization of 28560

Prime factors of 28560 are 2, 3, 5, 7, 17. Prime factorization of 28560 in exponential form is:

28560 = 2⁴ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 28567

Prime factors of 28567 are 7, 11, 53. Prime factorization of 28567 in exponential form is:

28567 = 7² × 11¹ × 53¹

Step-3: Factors of 28560

List of positive integer factors of 28560 that divides 28560 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 20, 21, 24, 28, 30, 34, 35, 40, 42, 48, 51, 56, 60, 68, 70, 80, 84, 85, 102, 105, 112, 119, 120, 136, 140, 168, 170, 204, 210, 238, 240, 255, 272, 280, 336, 340, 357, 408, 420, 476, 510, 560, 595, 680, 714, 816, 840, 952, 1020, 1190, 1360, 1428, 1680, 1785, 1904, 2040, 2380, 2856, 3570, 4080, 4760, 5712, 7140, 9520, 14280

Step-4: Factors of 28567

List of positive integer factors of 28567 that divides 28560 without a remainder.

1, 7, 11, 49, 53, 77, 371, 539, 583, 2597, 4081

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28560 and 28567. The biggest common factor number is the GCF number.
So the greatest common factor 28560 and 28567 is 7.

Also check out the Least Common Multiple of 28560 and 28567