What is the Greatest Common Factor of 27342 and 27360?

Greatest common factor (GCF) of 27342 and 27360 is 18.

GCF(27342,27360) = 18

We will now calculate the prime factors of 27342 and 27360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27342 and 27360.

How to find the GCF of 27342 and 27360?

We will first find the prime factorization of 27342 and 27360. After we will calculate the factors of 27342 and 27360 and find the biggest common factor number .

Step-1: Prime Factorization of 27342

Prime factors of 27342 are 2, 3, 7, 31. Prime factorization of 27342 in exponential form is:

27342 = 2¹ × 3² × 7² × 31¹

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 27342

List of positive integer factors of 27342 that divides 27342 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 31, 42, 49, 62, 63, 93, 98, 126, 147, 186, 217, 279, 294, 434, 441, 558, 651, 882, 1302, 1519, 1953, 3038, 3906, 4557, 9114, 13671

Step-4: Factors of 27360

List of positive integer factors of 27360 that divides 27342 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 27342 and 27360. The biggest common factor number is the GCF number.
So the greatest common factor 27342 and 27360 is 18.

Also check out the Least Common Multiple of 27342 and 27360