What is the Greatest Common Factor of 12738 and 12754?

Greatest common factor (GCF) of 12738 and 12754 is 2.

GCF(12738,12754) = 2

We will now calculate the prime factors of 12738 and 12754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12738 and 12754.

How to find the GCF of 12738 and 12754?

We will first find the prime factorization of 12738 and 12754. After we will calculate the factors of 12738 and 12754 and find the biggest common factor number .

Step-1: Prime Factorization of 12738

Prime factors of 12738 are 2, 3, 11, 193. Prime factorization of 12738 in exponential form is:

12738 = 2¹ × 3¹ × 11¹ × 193¹

Step-2: Prime Factorization of 12754

Prime factors of 12754 are 2, 7, 911. Prime factorization of 12754 in exponential form is:

12754 = 2¹ × 7¹ × 911¹

Step-3: Factors of 12738

List of positive integer factors of 12738 that divides 12738 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 193, 386, 579, 1158, 2123, 4246, 6369

Step-4: Factors of 12754

List of positive integer factors of 12754 that divides 12738 without a remainder.

1, 2, 7, 14, 911, 1822, 6377

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12738 and 12754. The biggest common factor number is the GCF number.
So the greatest common factor 12738 and 12754 is 2.

Also check out the Least Common Multiple of 12738 and 12754