What is the Greatest Common Factor of 27344 and 27360?

Greatest common factor (GCF) of 27344 and 27360 is 16.

GCF(27344,27360) = 16

We will now calculate the prime factors of 27344 and 27360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27344 and 27360.

How to find the GCF of 27344 and 27360?

We will first find the prime factorization of 27344 and 27360. After we will calculate the factors of 27344 and 27360 and find the biggest common factor number .

Step-1: Prime Factorization of 27344

Prime factors of 27344 are 2, 1709. Prime factorization of 27344 in exponential form is:

27344 = 2⁴ × 1709¹

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 27344

List of positive integer factors of 27344 that divides 27344 without a remainder.

1, 2, 4, 8, 16, 1709, 3418, 6836, 13672

Step-4: Factors of 27360

List of positive integer factors of 27360 that divides 27344 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 27344 and 27360. The biggest common factor number is the GCF number.
So the greatest common factor 27344 and 27360 is 16.

Also check out the Least Common Multiple of 27344 and 27360