What is the Greatest Common Factor of 13804 and 13821?

Greatest common factor (GCF) of 13804 and 13821 is 17.

GCF(13804,13821) = 17

We will now calculate the prime factors of 13804 and 13821, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13804 and 13821.

How to find the GCF of 13804 and 13821?

We will first find the prime factorization of 13804 and 13821. After we will calculate the factors of 13804 and 13821 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 13821

Prime factors of 13821 are 3, 17, 271. Prime factorization of 13821 in exponential form is:

13821 = 3¹ × 17¹ × 271¹

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 13821

List of positive integer factors of 13821 that divides 13804 without a remainder.

1, 3, 17, 51, 271, 813, 4607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13804 and 13821. The biggest common factor number is the GCF number.
So the greatest common factor 13804 and 13821 is 17.

Also check out the Least Common Multiple of 13804 and 13821