What is the Greatest Common Factor of 27830 and 27840?

Greatest common factor (GCF) of 27830 and 27840 is 10.

GCF(27830,27840) = 10

We will now calculate the prime factors of 27830 and 27840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27830 and 27840.

How to find the GCF of 27830 and 27840?

We will first find the prime factorization of 27830 and 27840. After we will calculate the factors of 27830 and 27840 and find the biggest common factor number .

Step-1: Prime Factorization of 27830

Prime factors of 27830 are 2, 5, 11, 23. Prime factorization of 27830 in exponential form is:

27830 = 2¹ × 5¹ × 11² × 23¹

Step-2: 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-3: Factors of 27830

List of positive integer factors of 27830 that divides 27830 without a remainder.

1, 2, 5, 10, 11, 22, 23, 46, 55, 110, 115, 121, 230, 242, 253, 506, 605, 1210, 1265, 2530, 2783, 5566, 13915

Step-4: Factors of 27840

List of positive integer factors of 27840 that divides 27830 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27830 and 27840. The biggest common factor number is the GCF number.
So the greatest common factor 27830 and 27840 is 10.

Also check out the Least Common Multiple of 27830 and 27840