What is the Greatest Common Factor of 13804 and 13822?

Greatest common factor (GCF) of 13804 and 13822 is 2.

GCF(13804,13822) = 2

We will now calculate the prime factors of 13804 and 13822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13804 and 13822.

How to find the GCF of 13804 and 13822?

We will first find the prime factorization of 13804 and 13822. After we will calculate the factors of 13804 and 13822 and find the biggest common factor number .

Step-1: Prime Factorization of 13804

Prime factors of 13804 are 2, 7, 17, 29. Prime factorization of 13804 in exponential form is:

13804 = 2² × 7¹ × 17¹ × 29¹

Step-2: Prime Factorization of 13822

Prime factors of 13822 are 2, 6911. Prime factorization of 13822 in exponential form is:

13822 = 2¹ × 6911¹

Step-3: Factors of 13804

List of positive integer factors of 13804 that divides 13804 without a remainder.

1, 2, 4, 7, 14, 17, 28, 29, 34, 58, 68, 116, 119, 203, 238, 406, 476, 493, 812, 986, 1972, 3451, 6902

Step-4: Factors of 13822

List of positive integer factors of 13822 that divides 13804 without a remainder.

1, 2, 6911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13804 and 13822. The biggest common factor number is the GCF number.
So the greatest common factor 13804 and 13822 is 2.

Also check out the Least Common Multiple of 13804 and 13822