What is the Greatest Common Factor of 13827 and 13838?

Greatest common factor (GCF) of 13827 and 13838 is 11.

GCF(13827,13838) = 11

We will now calculate the prime factors of 13827 and 13838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13827 and 13838.

How to find the GCF of 13827 and 13838?

We will first find the prime factorization of 13827 and 13838. After we will calculate the factors of 13827 and 13838 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13838

Prime factors of 13838 are 2, 11, 17, 37. Prime factorization of 13838 in exponential form is:

13838 = 2¹ × 11¹ × 17¹ × 37¹

Step-3: Factors of 13827

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

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

Step-4: Factors of 13838

List of positive integer factors of 13838 that divides 13827 without a remainder.

1, 2, 11, 17, 22, 34, 37, 74, 187, 374, 407, 629, 814, 1258, 6919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13827 and 13838. The biggest common factor number is the GCF number.
So the greatest common factor 13827 and 13838 is 11.

Also check out the Least Common Multiple of 13827 and 13838