What is the Greatest Common Factor of 28560 and 28575?

Greatest common factor (GCF) of 28560 and 28575 is 15.

GCF(28560,28575) = 15

We will now calculate the prime factors of 28560 and 28575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28560 and 28575.

How to find the GCF of 28560 and 28575?

We will first find the prime factorization of 28560 and 28575. After we will calculate the factors of 28560 and 28575 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 28575

Prime factors of 28575 are 3, 5, 127. Prime factorization of 28575 in exponential form is:

28575 = 3² × 5² × 127¹

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 28575

List of positive integer factors of 28575 that divides 28560 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 127, 225, 381, 635, 1143, 1905, 3175, 5715, 9525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28560 and 28575. The biggest common factor number is the GCF number.
So the greatest common factor 28560 and 28575 is 15.

Also check out the Least Common Multiple of 28560 and 28575