What is the Greatest Common Factor of 27348 and 27360?

Greatest common factor (GCF) of 27348 and 27360 is 12.

GCF(27348,27360) = 12

We will now calculate the prime factors of 27348 and 27360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27348 and 27360.

How to find the GCF of 27348 and 27360?

We will first find the prime factorization of 27348 and 27360. After we will calculate the factors of 27348 and 27360 and find the biggest common factor number .

Step-1: Prime Factorization of 27348

Prime factors of 27348 are 2, 3, 43, 53. Prime factorization of 27348 in exponential form is:

27348 = 2² × 3¹ × 43¹ × 53¹

Step-2: 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-3: Factors of 27348

List of positive integer factors of 27348 that divides 27348 without a remainder.

1, 2, 3, 4, 6, 12, 43, 53, 86, 106, 129, 159, 172, 212, 258, 318, 516, 636, 2279, 4558, 6837, 9116, 13674

Step-4: Factors of 27360

List of positive integer factors of 27360 that divides 27348 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27348 and 27360. The biggest common factor number is the GCF number.
So the greatest common factor 27348 and 27360 is 12.

Also check out the Least Common Multiple of 27348 and 27360