What is the Greatest Common Factor of 28544 and 28560?

Greatest common factor (GCF) of 28544 and 28560 is 16.

GCF(28544,28560) = 16

We will now calculate the prime factors of 28544 and 28560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28544 and 28560.

How to find the GCF of 28544 and 28560?

We will first find the prime factorization of 28544 and 28560. After we will calculate the factors of 28544 and 28560 and find the biggest common factor number .

Step-1: Prime Factorization of 28544

Prime factors of 28544 are 2, 223. Prime factorization of 28544 in exponential form is:

28544 = 2⁷ × 223¹

Step-2: 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-3: Factors of 28544

List of positive integer factors of 28544 that divides 28544 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 223, 446, 892, 1784, 3568, 7136, 14272

Step-4: Factors of 28560

List of positive integer factors of 28560 that divides 28544 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28544 and 28560. The biggest common factor number is the GCF number.
So the greatest common factor 28544 and 28560 is 16.

Also check out the Least Common Multiple of 28544 and 28560