What is the Greatest Common Factor of 28140 and 28160?

Greatest common factor (GCF) of 28140 and 28160 is 20.

GCF(28140,28160) = 20

We will now calculate the prime factors of 28140 and 28160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28140 and 28160.

How to find the GCF of 28140 and 28160?

We will first find the prime factorization of 28140 and 28160. After we will calculate the factors of 28140 and 28160 and find the biggest common factor number .

Step-1: Prime Factorization of 28140

Prime factors of 28140 are 2, 3, 5, 7, 67. Prime factorization of 28140 in exponential form is:

28140 = 2² × 3¹ × 5¹ × 7¹ × 67¹

Step-2: Prime Factorization of 28160

Prime factors of 28160 are 2, 5, 11. Prime factorization of 28160 in exponential form is:

28160 = 2⁹ × 5¹ × 11¹

Step-3: Factors of 28140

List of positive integer factors of 28140 that divides 28140 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 67, 70, 84, 105, 134, 140, 201, 210, 268, 335, 402, 420, 469, 670, 804, 938, 1005, 1340, 1407, 1876, 2010, 2345, 2814, 4020, 4690, 5628, 7035, 9380, 14070

Step-4: Factors of 28160

List of positive integer factors of 28160 that divides 28140 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 128, 160, 176, 220, 256, 320, 352, 440, 512, 640, 704, 880, 1280, 1408, 1760, 2560, 2816, 3520, 5632, 7040, 14080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28140 and 28160. The biggest common factor number is the GCF number.
So the greatest common factor 28140 and 28160 is 20.

Also check out the Least Common Multiple of 28140 and 28160