What is the Greatest Common Factor of 12814 and 12834?

Greatest common factor (GCF) of 12814 and 12834 is 2.

GCF(12814,12834) = 2

We will now calculate the prime factors of 12814 and 12834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12814 and 12834.

How to find the GCF of 12814 and 12834?

We will first find the prime factorization of 12814 and 12834. After we will calculate the factors of 12814 and 12834 and find the biggest common factor number .

Step-1: Prime Factorization of 12814

Prime factors of 12814 are 2, 43, 149. Prime factorization of 12814 in exponential form is:

12814 = 2¹ × 43¹ × 149¹

Step-2: Prime Factorization of 12834

Prime factors of 12834 are 2, 3, 23, 31. Prime factorization of 12834 in exponential form is:

12834 = 2¹ × 3² × 23¹ × 31¹

Step-3: Factors of 12814

List of positive integer factors of 12814 that divides 12814 without a remainder.

1, 2, 43, 86, 149, 298, 6407

Step-4: Factors of 12834

List of positive integer factors of 12834 that divides 12814 without a remainder.

1, 2, 3, 6, 9, 18, 23, 31, 46, 62, 69, 93, 138, 186, 207, 279, 414, 558, 713, 1426, 2139, 4278, 6417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12814 and 12834. The biggest common factor number is the GCF number.
So the greatest common factor 12814 and 12834 is 2.

Also check out the Least Common Multiple of 12814 and 12834