What is the Greatest Common Factor of 27840 and 27860?

Greatest common factor (GCF) of 27840 and 27860 is 20.

GCF(27840,27860) = 20

We will now calculate the prime factors of 27840 and 27860, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27840 and 27860.

How to find the GCF of 27840 and 27860?

We will first find the prime factorization of 27840 and 27860. After we will calculate the factors of 27840 and 27860 and find the biggest common factor number .

Step-1: Prime Factorization of 27840

Prime factors of 27840 are 2, 3, 5, 29. Prime factorization of 27840 in exponential form is:

27840 = 2⁶ × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 27860

Prime factors of 27860 are 2, 5, 7, 199. Prime factorization of 27860 in exponential form is:

27860 = 2² × 5¹ × 7¹ × 199¹

Step-3: Factors of 27840

List of positive integer factors of 27840 that divides 27840 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80, 87, 96, 116, 120, 145, 160, 174, 192, 232, 240, 290, 320, 348, 435, 464, 480, 580, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 2320, 2784, 3480, 4640, 5568, 6960, 9280, 13920

Step-4: Factors of 27860

List of positive integer factors of 27860 that divides 27840 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 199, 398, 796, 995, 1393, 1990, 2786, 3980, 5572, 6965, 13930

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27840 and 27860. The biggest common factor number is the GCF number.
So the greatest common factor 27840 and 27860 is 20.

Also check out the Least Common Multiple of 27840 and 27860