What is the Greatest Common Factor of 28560 and 28565?

Greatest common factor (GCF) of 28560 and 28565 is 5.

GCF(28560,28565) = 5

We will now calculate the prime factors of 28560 and 28565, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28560 and 28565.

How to find the GCF of 28560 and 28565?

We will first find the prime factorization of 28560 and 28565. After we will calculate the factors of 28560 and 28565 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 28565

Prime factors of 28565 are 5, 29, 197. Prime factorization of 28565 in exponential form is:

28565 = 5¹ × 29¹ × 197¹

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 28565

List of positive integer factors of 28565 that divides 28560 without a remainder.

1, 5, 29, 145, 197, 985, 5713

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28560 and 28565. The biggest common factor number is the GCF number.
So the greatest common factor 28560 and 28565 is 5.

Also check out the Least Common Multiple of 28560 and 28565