What is the Greatest Common Factor of 27360 and 27380?

Greatest common factor (GCF) of 27360 and 27380 is 20.

GCF(27360,27380) = 20

We will now calculate the prime factors of 27360 and 27380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27360 and 27380.

How to find the GCF of 27360 and 27380?

We will first find the prime factorization of 27360 and 27380. After we will calculate the factors of 27360 and 27380 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 27380

Prime factors of 27380 are 2, 5, 37. Prime factorization of 27380 in exponential form is:

27380 = 2² × 5¹ × 37²

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 27380

List of positive integer factors of 27380 that divides 27360 without a remainder.

1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740, 1369, 2738, 5476, 6845, 13690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27360 and 27380. The biggest common factor number is the GCF number.
So the greatest common factor 27360 and 27380 is 20.

Also check out the Least Common Multiple of 27360 and 27380