What is the Greatest Common Factor of 12546 and 12563?

Greatest common factor (GCF) of 12546 and 12563 is 17.

GCF(12546,12563) = 17

We will now calculate the prime factors of 12546 and 12563, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12546 and 12563.

How to find the GCF of 12546 and 12563?

We will first find the prime factorization of 12546 and 12563. After we will calculate the factors of 12546 and 12563 and find the biggest common factor number .

Step-1: Prime Factorization of 12546

Prime factors of 12546 are 2, 3, 17, 41. Prime factorization of 12546 in exponential form is:

12546 = 2¹ × 3² × 17¹ × 41¹

Step-2: Prime Factorization of 12563

Prime factors of 12563 are 17, 739. Prime factorization of 12563 in exponential form is:

12563 = 17¹ × 739¹

Step-3: Factors of 12546

List of positive integer factors of 12546 that divides 12546 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 41, 51, 82, 102, 123, 153, 246, 306, 369, 697, 738, 1394, 2091, 4182, 6273

Step-4: Factors of 12563

List of positive integer factors of 12563 that divides 12546 without a remainder.

1, 17, 739

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12546 and 12563. The biggest common factor number is the GCF number.
So the greatest common factor 12546 and 12563 is 17.

Also check out the Least Common Multiple of 12546 and 12563