What is the Greatest Common Factor of 12345 and 12357?

Greatest common factor (GCF) of 12345 and 12357 is 3.

GCF(12345,12357) = 3

We will now calculate the prime factors of 12345 and 12357, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12345 and 12357.

How to find the GCF of 12345 and 12357?

We will first find the prime factorization of 12345 and 12357. After we will calculate the factors of 12345 and 12357 and find the biggest common factor number .

Step-1: Prime Factorization of 12345

Prime factors of 12345 are 3, 5, 823. Prime factorization of 12345 in exponential form is:

12345 = 3¹ × 5¹ × 823¹

Step-2: Prime Factorization of 12357

Prime factors of 12357 are 3, 1373. Prime factorization of 12357 in exponential form is:

12357 = 3² × 1373¹

Step-3: Factors of 12345

List of positive integer factors of 12345 that divides 12345 without a remainder.

1, 3, 5, 15, 823, 2469, 4115

Step-4: Factors of 12357

List of positive integer factors of 12357 that divides 12345 without a remainder.

1, 3, 9, 1373, 4119

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12345 and 12357. The biggest common factor number is the GCF number.
So the greatest common factor 12345 and 12357 is 3.

Also check out the Least Common Multiple of 12345 and 12357