What is the Greatest Common Factor of 12345 and 12354?

Greatest common factor (GCF) of 12345 and 12354 is 3.

GCF(12345,12354) = 3

We will now calculate the prime factors of 12345 and 12354, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12345 and 12354.

How to find the GCF of 12345 and 12354?

We will first find the prime factorization of 12345 and 12354. After we will calculate the factors of 12345 and 12354 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 12354

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

12354 = 2¹ × 3¹ × 29¹ × 71¹

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 12354

List of positive integer factors of 12354 that divides 12345 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12345 and 12354. The biggest common factor number is the GCF number.
So the greatest common factor 12345 and 12354 is 3.

Also check out the Least Common Multiple of 12345 and 12354