What is the Greatest Common Factor of 12354 and 12369?

Greatest common factor (GCF) of 12354 and 12369 is 3.

GCF(12354,12369) = 3

We will now calculate the prime factors of 12354 and 12369, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12354 and 12369.

How to find the GCF of 12354 and 12369?

We will first find the prime factorization of 12354 and 12369. After we will calculate the factors of 12354 and 12369 and find the biggest common factor number .

Step-1: Prime Factorization of 12354

Prime factors of 12354 are 2, 3, 29, 71. Prime factorization of 12354 in exponential form is:

12354 = 2¹ × 3¹ × 29¹ × 71¹

Step-2: 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-3: Factors of 12354

List of positive integer factors of 12354 that divides 12354 without a remainder.

1, 2, 3, 6, 29, 58, 71, 87, 142, 174, 213, 426, 2059, 4118, 6177

Step-4: Factors of 12369

List of positive integer factors of 12369 that divides 12354 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12354 and 12369. The biggest common factor number is the GCF number.
So the greatest common factor 12354 and 12369 is 3.

Also check out the Least Common Multiple of 12354 and 12369