What is the Greatest Common Factor of 27822 and 27840?

Greatest common factor (GCF) of 27822 and 27840 is 6.

GCF(27822,27840) = 6

We will now calculate the prime factors of 27822 and 27840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27822 and 27840.

How to find the GCF of 27822 and 27840?

We will first find the prime factorization of 27822 and 27840. After we will calculate the factors of 27822 and 27840 and find the biggest common factor number .

Step-1: Prime Factorization of 27822

Prime factors of 27822 are 2, 3, 4637. Prime factorization of 27822 in exponential form is:

27822 = 2¹ × 3¹ × 4637¹

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 27822

List of positive integer factors of 27822 that divides 27822 without a remainder.

1, 2, 3, 6, 4637, 9274, 13911

Step-4: Factors of 27840

List of positive integer factors of 27840 that divides 27822 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 27822 and 27840. The biggest common factor number is the GCF number.
So the greatest common factor 27822 and 27840 is 6.

Also check out the Least Common Multiple of 27822 and 27840