What is the Greatest Common Factor of 13838 and 13842?

Greatest common factor (GCF) of 13838 and 13842 is 2.

GCF(13838,13842) = 2

We will now calculate the prime factors of 13838 and 13842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13838 and 13842.

How to find the GCF of 13838 and 13842?

We will first find the prime factorization of 13838 and 13842. After we will calculate the factors of 13838 and 13842 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13842

Prime factors of 13842 are 2, 3, 769. Prime factorization of 13842 in exponential form is:

13842 = 2¹ × 3² × 769¹

Step-3: Factors of 13838

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

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

Step-4: Factors of 13842

List of positive integer factors of 13842 that divides 13838 without a remainder.

1, 2, 3, 6, 9, 18, 769, 1538, 2307, 4614, 6921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13838 and 13842. The biggest common factor number is the GCF number.
So the greatest common factor 13838 and 13842 is 2.

Also check out the Least Common Multiple of 13838 and 13842