What is the Greatest Common Factor of 12306 and 12312?

Greatest common factor (GCF) of 12306 and 12312 is 6.

GCF(12306,12312) = 6

We will now calculate the prime factors of 12306 and 12312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12306 and 12312.

How to find the GCF of 12306 and 12312?

We will first find the prime factorization of 12306 and 12312. After we will calculate the factors of 12306 and 12312 and find the biggest common factor number .

Step-1: Prime Factorization of 12306

Prime factors of 12306 are 2, 3, 7, 293. Prime factorization of 12306 in exponential form is:

12306 = 2¹ × 3¹ × 7¹ × 293¹

Step-2: Prime Factorization of 12312

Prime factors of 12312 are 2, 3, 19. Prime factorization of 12312 in exponential form is:

12312 = 2³ × 3⁴ × 19¹

Step-3: Factors of 12306

List of positive integer factors of 12306 that divides 12306 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 293, 586, 879, 1758, 2051, 4102, 6153

Step-4: Factors of 12312

List of positive integer factors of 12312 that divides 12306 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 81, 108, 114, 152, 162, 171, 216, 228, 324, 342, 456, 513, 648, 684, 1026, 1368, 1539, 2052, 3078, 4104, 6156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12306 and 12312. The biggest common factor number is the GCF number.
So the greatest common factor 12306 and 12312 is 6.

Also check out the Least Common Multiple of 12306 and 12312