What is the Greatest Common Factor of 13821 and 13827?

Greatest common factor (GCF) of 13821 and 13827 is 3.

GCF(13821,13827) = 3

We will now calculate the prime factors of 13821 and 13827, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13821 and 13827.

How to find the GCF of 13821 and 13827?

We will first find the prime factorization of 13821 and 13827. After we will calculate the factors of 13821 and 13827 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13827

Prime factors of 13827 are 3, 11, 419. Prime factorization of 13827 in exponential form is:

13827 = 3¹ × 11¹ × 419¹

Step-3: Factors of 13821

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

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

Step-4: Factors of 13827

List of positive integer factors of 13827 that divides 13821 without a remainder.

1, 3, 11, 33, 419, 1257, 4609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13821 and 13827. The biggest common factor number is the GCF number.
So the greatest common factor 13821 and 13827 is 3.

Also check out the Least Common Multiple of 13821 and 13827