What is the Greatest Common Factor of 12369 and 12375?

Greatest common factor (GCF) of 12369 and 12375 is 3.

GCF(12369,12375) = 3

We will now calculate the prime factors of 12369 and 12375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12369 and 12375.

How to find the GCF of 12369 and 12375?

We will first find the prime factorization of 12369 and 12375. After we will calculate the factors of 12369 and 12375 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 12375

Prime factors of 12375 are 3, 5, 11. Prime factorization of 12375 in exponential form is:

12375 = 3² × 5³ × 11¹

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 12375

List of positive integer factors of 12375 that divides 12369 without a remainder.

1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 125, 165, 225, 275, 375, 495, 825, 1125, 1375, 2475, 4125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12369 and 12375. The biggest common factor number is the GCF number.
So the greatest common factor 12369 and 12375 is 3.

Also check out the Least Common Multiple of 12369 and 12375