What is the Greatest Common Factor of 13858 and 13872?

Greatest common factor (GCF) of 13858 and 13872 is 2.

GCF(13858,13872) = 2

We will now calculate the prime factors of 13858 and 13872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13858 and 13872.

How to find the GCF of 13858 and 13872?

We will first find the prime factorization of 13858 and 13872. After we will calculate the factors of 13858 and 13872 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13872

Prime factors of 13872 are 2, 3, 17. Prime factorization of 13872 in exponential form is:

13872 = 2⁴ × 3¹ × 17²

Step-3: Factors of 13858

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

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

Step-4: Factors of 13872

List of positive integer factors of 13872 that divides 13858 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 289, 408, 578, 816, 867, 1156, 1734, 2312, 3468, 4624, 6936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13858 and 13872. The biggest common factor number is the GCF number.
So the greatest common factor 13858 and 13872 is 2.

Also check out the Least Common Multiple of 13858 and 13872