What is the Greatest Common Factor of 12738 and 12749?

Greatest common factor (GCF) of 12738 and 12749 is 11.

GCF(12738,12749) = 11

We will now calculate the prime factors of 12738 and 12749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12738 and 12749.

How to find the GCF of 12738 and 12749?

We will first find the prime factorization of 12738 and 12749. After we will calculate the factors of 12738 and 12749 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 12749

Prime factors of 12749 are 11, 19, 61. Prime factorization of 12749 in exponential form is:

12749 = 11¹ × 19¹ × 61¹

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 12749

List of positive integer factors of 12749 that divides 12738 without a remainder.

1, 11, 19, 61, 209, 671, 1159

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12738 and 12749. The biggest common factor number is the GCF number.
So the greatest common factor 12738 and 12749 is 11.

Also check out the Least Common Multiple of 12738 and 12749