What is the Greatest Common Factor of 27360 and 27378?

Greatest common factor (GCF) of 27360 and 27378 is 18.

GCF(27360,27378) = 18

We will now calculate the prime factors of 27360 and 27378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27360 and 27378.

How to find the GCF of 27360 and 27378?

We will first find the prime factorization of 27360 and 27378. After we will calculate the factors of 27360 and 27378 and find the biggest common factor number .

Step-1: Prime Factorization of 27360

Prime factors of 27360 are 2, 3, 5, 19. Prime factorization of 27360 in exponential form is:

27360 = 2⁵ × 3² × 5¹ × 19¹

Step-2: Prime Factorization of 27378

Prime factors of 27378 are 2, 3, 13. Prime factorization of 27378 in exponential form is:

27378 = 2¹ × 3⁴ × 13²

Step-3: Factors of 27360

List of positive integer factors of 27360 that divides 27360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 32, 36, 38, 40, 45, 48, 57, 60, 72, 76, 80, 90, 95, 96, 114, 120, 144, 152, 160, 171, 180, 190, 228, 240, 285, 288, 304, 342, 360, 380, 456, 480, 570, 608, 684, 720, 760, 855, 912, 1140, 1368, 1440, 1520, 1710, 1824, 2280, 2736, 3040, 3420, 4560, 5472, 6840, 9120, 13680

Step-4: Factors of 27378

List of positive integer factors of 27378 that divides 27360 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 169, 234, 338, 351, 507, 702, 1014, 1053, 1521, 2106, 3042, 4563, 9126, 13689

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27360 and 27378. The biggest common factor number is the GCF number.
So the greatest common factor 27360 and 27378 is 18.

Also check out the Least Common Multiple of 27360 and 27378