What is the Greatest Common Factor of 12802 and 12814?

Greatest common factor (GCF) of 12802 and 12814 is 2.

GCF(12802,12814) = 2

We will now calculate the prime factors of 12802 and 12814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12802 and 12814.

How to find the GCF of 12802 and 12814?

We will first find the prime factorization of 12802 and 12814. After we will calculate the factors of 12802 and 12814 and find the biggest common factor number .

Step-1: Prime Factorization of 12802

Prime factors of 12802 are 2, 37, 173. Prime factorization of 12802 in exponential form is:

12802 = 2¹ × 37¹ × 173¹

Step-2: 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-3: Factors of 12802

List of positive integer factors of 12802 that divides 12802 without a remainder.

1, 2, 37, 74, 173, 346, 6401

Step-4: Factors of 12814

List of positive integer factors of 12814 that divides 12802 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12802 and 12814. The biggest common factor number is the GCF number.
So the greatest common factor 12802 and 12814 is 2.

Also check out the Least Common Multiple of 12802 and 12814