What is the Greatest Common Factor of 28560 and 28569?

Greatest common factor (GCF) of 28560 and 28569 is 3.

GCF(28560,28569) = 3

We will now calculate the prime factors of 28560 and 28569, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28560 and 28569.

How to find the GCF of 28560 and 28569?

We will first find the prime factorization of 28560 and 28569. After we will calculate the factors of 28560 and 28569 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 28569

Prime factors of 28569 are 3, 89, 107. Prime factorization of 28569 in exponential form is:

28569 = 3¹ × 89¹ × 107¹

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 28569

List of positive integer factors of 28569 that divides 28560 without a remainder.

1, 3, 89, 107, 267, 321, 9523

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28560 and 28569. The biggest common factor number is the GCF number.
So the greatest common factor 28560 and 28569 is 3.

Also check out the Least Common Multiple of 28560 and 28569