What is the Greatest Common Factor of 12369 and 12384?

Greatest common factor (GCF) of 12369 and 12384 is 3.

GCF(12369,12384) = 3

We will now calculate the prime factors of 12369 and 12384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12369 and 12384.

How to find the GCF of 12369 and 12384?

We will first find the prime factorization of 12369 and 12384. After we will calculate the factors of 12369 and 12384 and find the biggest common factor number .

Step-1: Prime Factorization of 12369

Prime factors of 12369 are 3, 7, 19, 31. Prime factorization of 12369 in exponential form is:

12369 = 3¹ × 7¹ × 19¹ × 31¹

Step-2: Prime Factorization of 12384

Prime factors of 12384 are 2, 3, 43. Prime factorization of 12384 in exponential form is:

12384 = 2⁵ × 3² × 43¹

Step-3: Factors of 12369

List of positive integer factors of 12369 that divides 12369 without a remainder.

1, 3, 7, 19, 21, 31, 57, 93, 133, 217, 399, 589, 651, 1767, 4123

Step-4: Factors of 12384

List of positive integer factors of 12384 that divides 12369 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 72, 86, 96, 129, 144, 172, 258, 288, 344, 387, 516, 688, 774, 1032, 1376, 1548, 2064, 3096, 4128, 6192

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12369 and 12384. The biggest common factor number is the GCF number.
So the greatest common factor 12369 and 12384 is 3.

Also check out the Least Common Multiple of 12369 and 12384