What is the Greatest Common Factor of 12638 and 12642?

Greatest common factor (GCF) of 12638 and 12642 is 2.

GCF(12638,12642) = 2

We will now calculate the prime factors of 12638 and 12642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12638 and 12642.

How to find the GCF of 12638 and 12642?

We will first find the prime factorization of 12638 and 12642. After we will calculate the factors of 12638 and 12642 and find the biggest common factor number .

Step-1: Prime Factorization of 12638

Prime factors of 12638 are 2, 71, 89. Prime factorization of 12638 in exponential form is:

12638 = 2¹ × 71¹ × 89¹

Step-2: Prime Factorization of 12642

Prime factors of 12642 are 2, 3, 7, 43. Prime factorization of 12642 in exponential form is:

12642 = 2¹ × 3¹ × 7² × 43¹

Step-3: Factors of 12638

List of positive integer factors of 12638 that divides 12638 without a remainder.

1, 2, 71, 89, 142, 178, 6319

Step-4: Factors of 12642

List of positive integer factors of 12642 that divides 12638 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 43, 49, 86, 98, 129, 147, 258, 294, 301, 602, 903, 1806, 2107, 4214, 6321

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12638 and 12642. The biggest common factor number is the GCF number.
So the greatest common factor 12638 and 12642 is 2.

Also check out the Least Common Multiple of 12638 and 12642