What is the Greatest Common Factor of 28540 and 28560?

Greatest common factor (GCF) of 28540 and 28560 is 20.

GCF(28540,28560) = 20

We will now calculate the prime factors of 28540 and 28560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28540 and 28560.

How to find the GCF of 28540 and 28560?

We will first find the prime factorization of 28540 and 28560. After we will calculate the factors of 28540 and 28560 and find the biggest common factor number .

Step-1: Prime Factorization of 28540

Prime factors of 28540 are 2, 5, 1427. Prime factorization of 28540 in exponential form is:

28540 = 2² × 5¹ × 1427¹

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 28540

List of positive integer factors of 28540 that divides 28540 without a remainder.

1, 2, 4, 5, 10, 20, 1427, 2854, 5708, 7135, 14270

Step-4: Factors of 28560

List of positive integer factors of 28560 that divides 28540 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 28540 and 28560. The biggest common factor number is the GCF number.
So the greatest common factor 28540 and 28560 is 20.

Also check out the Least Common Multiple of 28540 and 28560