What is the Greatest Common Factor of 13838 and 13858?

Greatest common factor (GCF) of 13838 and 13858 is 2.

GCF(13838,13858) = 2

We will now calculate the prime factors of 13838 and 13858, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13838 and 13858.

How to find the GCF of 13838 and 13858?

We will first find the prime factorization of 13838 and 13858. After we will calculate the factors of 13838 and 13858 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 13858

Prime factors of 13858 are 2, 13, 41. Prime factorization of 13858 in exponential form is:

13858 = 2¹ × 13² × 41¹

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 13858

List of positive integer factors of 13858 that divides 13838 without a remainder.

1, 2, 13, 26, 41, 82, 169, 338, 533, 1066, 6929

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13838 and 13858. The biggest common factor number is the GCF number.
So the greatest common factor 13838 and 13858 is 2.

Also check out the Least Common Multiple of 13838 and 13858